Investigações da dinâmica crítica em modelos de magnetismo, para tempos curtos, têm aparecido com grande freqüência na literatura. Essa técnica foi descoberta por Li, Schülke e Zheng que, inspirados em trabalhos anteriores de Huse e Janssen et al., mostraram que generalizações de grandezas como a magnetização e o cumulante de Binder exibem comportamento universal já no início da simulação. O estudo da criticalidade em tempos curtos proporciona um caminho alternativo para a estimativa do expoente z, além de permitir o cálculo de um novo expoente dinâmico θ, associado ao comportamento anômalo da magnetização. Da mesma forma, simulações dependentes do tempo tornaram-se ferramenta útil para estudar transições de fase em autômatos celulares e modelos de spin. Em particular, as melhores estimativas para o expoente z do Ising bidimensional foram obtidas por meio da técnica de propagação de danos, introduzida por Kauffman no estudo de autômatos e mais tarde generalizada para modelos de spin. Na primeira parte deste trabalho utilizamos o método Monte Carlo em tempos curtos para investigar o modelo de Baxter-Wu, definido em uma rede bidimensional triangular com variáveis do tipo Ising, acopladas por interações de três corpos. Obtivemos os expoentes críticos dinâmicos z e θ além dos índices críticos estáticos ß e Nû. Os resultados não corroboram aqueles recentemente obtidos por Santos e Figueiredo para o expoente z. Na segunda parte do trabalho, investigamos a propagação de danos no modelo de Ising unidimensional submetido a duas dinâmicas propostas por Hinrichsen e Domany (HD). Em particular, nós estudamos o efeito da atualização síncrona (paralela) e assíncrona (dinâmica contínua) sobre o espalhamento do dano. Mostramos que o dano não se propaga quando a segunda dinâmica é implementada de forma assíncrona. Também mostramos que as regras para atualização do dano produzidas por essa dinâmica, quando a temperatura vai a infinito e um certo parâmetro Lambda é igual a zero, são equivalentes àquelas do bem conhecido autômato celular (modelo A) de Grassberger. / Short-time simulations have been used with great frequency in the literature. That technique was discovered by Li, Shülke and Zheng that, inspired in previous works by Huse and Janssen et al., showed that generalizations of quantities like magnetization and the Binder´s cumulant exhibit universal behavior in the beginning of the simulation (early time behavior). The study of criticality in short-times provides an alternative way to estimate the dynamic critical exponent z, besides allowing the calculation of a new dynamic exponent θ, associated to the anomalous behavior of the magnetization. In the same way, time-dependent simulations became a useful tool to study phase transitions in cellular automata and also for spin models. In fact, the best estimates for the exponent z of the two-dimensional Ising model were obtained through the technique of damage spreading, introduced by Kauffman in the study of cellular automata, later widespread for spin models. In the first part of this work we used short-time Monte Carlo simulations to investigate the Baxter-Wu model, defined in a triangular lattice whose variables are Ising-like coupled by triplet interactions. We have obtained estimates for the dynamic critical exponents z and θ besides static exponents ß e Nû. Our results do not corroborate recent estimates by Santos and Figueiredo for the critical exponent z. In the second part of this work, we investigated the damage spreading in the one-dimensional Ising model under two dynamics introduced by Hinrichsen and Domany (HD). In particular, we study the effects of synchronous (parallel) and asynchronous (continuous dynamics) updating on the spreading properties. We showed that the damage does not spread when the second dynamic is implemented in an asynchronous way. We found that the rules for updating the damage produced by this dynamic, as the temperature goes to infinity and a certain parameter Lambda is zero, are equivalent to those of Grassberger’s well-known model A cellular automaton.

Com os avanços em eletrônica analógica e digital dos últimos 50 anos, a neurociência ganhou grande momentum e nasceu uma de suas áreas que atualmente mais recebe financiamento: neurociência computacional. Estudos nessa área, ainda considerada recente, vão desde estudos moleculares de trocas iônicas por canais iônicos (escala nanométrica), até influências de populações neurais no comportamento de grandes mamíferos (escala de até metros). O coração da neurociência computacional compreende técnicas inter- e multidisciplinares, envolvendo biologia de sistemas, bioquímica, modelagem matemática, estatística, termodinâmica, física estatística, etc. O impacto em áreas de grande interesse, como o desenvolvimento de fármacos e dispositivos militares, é a grande força motriz desta área. Especificamente para este último, a compreensão do código neural e como informação sensorial é trabalhada por populações de neurônios é essencial. E ainda estamos num estágio muito inicial de desvendar todo o funcionamento de muitos dos sistemas sensoriais mais complexos. Um exemplo é de um dos sentidos que parece existir desde as formas mais primitivas de vida: o olfato. Em mamíferos, o número de estudos parece sempre crescer com os anos. Ainda estamos, no entanto, longe de um consenso sobre o funcionamento de muitos dos mecanismos básicos do olfato. A literatura é extensa em termos bioquímicos e comportamental, mas reunir tudo em um único modelo é talvez o grande desafio atual. Nesta tese discuto, em duas partes, sistemas sensoriais seguindo uma linha bastante ligada ao sistema olfativo. Na primeira parte, um modelo formal que lembra o bulbo olfativo (de mamíferos) é considerado para investigar a relação entre a performance da codificação neural e a existência de uma dinâmica crítica. Em especial, discuto sobre últimos experimentos baseados em observações de leis de potência como evidências da existência de criticalidade e ótima performance em populações neurais. Mostro que, apesar de a performance das redes estar, sim, ligada ao ponto crítico do sistema, a existência de leis de potência não está ligada nem com tal ponto crítico, nem com a ótima performance. Experimentos recentes confirmam estas observações. Na segunda parte, discuto e proponho uma modelagem inicial para o órgão central do sentido olfativo em insetos: o Corpo Cogumelar. A novidade deste modelo está na integração temporal, além de conseguir tanto fazer reconhecimento de padrões (qual odor) e estimativa de concentrações de odores. Com este modelo, proponho uma explicação para uma recente observação de antecipação neural no Corpo Cogumelar, em que sua última camada paradoxalmente parece antecipar a primeira camada. Proponho a existência de um balanço entre agilidade do código neural contra acurácia no reconhecimento de padrões. Este balanço pode ser empiricamente testado. Também proponho a existência de um controle de ganho no Corpo Cogumelar que seria responsável pela manutenção dos ingredientes principais para reconhecimento de padrões e aprendizado. Ambas estas partes contribuem para o compreendimento de como sistemas sensoriais operam e quais os mecanismos fundamentais que os fornecem performance invejável. / With the advances in digital and analogical electronics in the last 50 years, neuroscience gained great momentum and one of its most well-financed sub-areas was born: computational neuroscience. Studies in this area, still considered recent by many, range from the ionic balance in the molecular level (scale of few nanometers), up to how neural populations influence behavior of large mammalians (scale of meters). The computational neuroscience core is highly based on inter- and multi-disciplinary techniques, involving systems biology, biochemistry, mathematical modeling, thermodynamics, statistical physics, etc. The impact in areas of current great interest, like in pharmaceutical drugs development and military devices, is its major flagship. Specifically for the later, deep understanding of neural code and how sensory information is filtered by neural populations is essential. And we are still grasping at the surface of really understanding many of the complex sensory systems we know. An example of such sensory modality that coexisted among all kinds of life forms is olfaction. In mammalians, the number of studies in this area seems to be growing steadily. However, we are still far from a complete agreement on how the basic mechanisms in olfaction work. There is a large literature of biochemical and behavioral studies, yet there is not a single model that comprises all this information and reproduces any olfactory system completely. In this thesis, I discuss in two parts sensory systems following a general line of argument based on olfaction. In the first part, a formal model that resembles the olfactory bulb (mammalians) is considered to investigate the relationship between performance in information coding and the existence of a critical dynamics. I show that, while the performance of neural networks may be intrinsically linked to a critical point, power laws are not exactly linked to neither critical points or performance optimization. Recent experiments corroborate this observation. In the second part, I discuss and propose a first dynamical model to the central organ responsible for olfactory learning in insects: the Mushroom Bodies. The novelty in this model is in the time integration, besides being able of pattern recognition (which odor) and concentration estimation at the same time. With this model, I propose an explanation for a seemingly paradoxical observation of coding anticipation in the Mushroom Bodies, where the last neural layer seems to trail the input layer. I propose the existence of a balance between accuracy and speed of pattern recognition in the Mushroom Bodies based on its fundamental morphological structure. I also propose the existence of a robust gain-control structure that sustain the key ingredients for pattern recognition and learning. This balance can be empirically tested. Both parts contribute to the understanding of the basic mechanisms behind sensory systems.

The present thesis reports computer simulation studies of several phase transition related phenomena in a range of soft-condensed matter systems. A coherent unifying theme of the thesis is the understanding of dynamics of phase transitions through free energy calculations using recently developed efficient non-Boltzmann sampling methods. Based on the system/phenomena of interest, the thesis has been classified into four major parts: I. Isotropic-nematic (IN) phase transition in liquid crystals. II. Nucleation phenomena in gas-liquid transition with particular emphasis on the systems close to the spinodal curve. III. Collapse transition in linear hydrocarbon (n-alkane) chains for a varying range of length, solvent and temperature. IV. Crystallization of unbranched polymer chains in dilute solution, with particular emphasis on the temperature dependent crossover between the rod-like crystalline state and spherical molten globule state. The thesis has been further divided into ten chapters running through the four parts mentioned before. In the following we provide a brief chapter-wise outline of the thesis. Part I deals with the power law relaxation and glassy dynamics in thermotropic liquid crystals close to the IN transition and consists of two chapters. To start with, Chapter I.1 provides an introduction to thermotropic liquid crystals. Here we briefly introduce various liquid crystalline phases, the order parameter used to characterize the IN transition, a few well established theoretical models, and we conclude with describing the recent experimental and computer simulation studies that have motivated the work described in the next chapter. In Chapter I.2, we present our molecular dynamics simulation studies on single particle and collective orientational dynamics across the IN transition for Lebwohl Lasher model, which is a well-known lattice model for thermotropic liquid crystals. Even this simplified model without any translational degrees of freedom successfully captures the short-tointermediate time power law decay recently observed in optical heterodyne detected optical Kerr effect (OHDOKE) measurements near the IN transition. The angular velocity time correlation function also exhibits a rather pronounced power law decay near the IN boundary. In the mean squared angular displacement at comparable time scales, we observe the emergence of a sub-diffusive regime which is followed by a super-diffusive regime before the onset of the longtime diffusive behavior. We observe signature of dynamical heterogeneity through pronounced non-Gaussian behavior in the orientational motion particularly at lower temperatures. Interestingly, this behavior closely resembles what is usually observed in supercooled liquids. We obtain the free energy as a function of orientational order parameter by the use of recently developed transition matrix Monte Carlo (TMMC) method. The free energy surface is flat for the system considered here and the barrier between isotropic and nematic phases is vanishingly small for this weakly first-order transition, hence allowing for large scale, collective, and correlated orientational density fluctuations. We attribute this large scale fluctuations as the reason for the observed power law decay of the orientational time correlation functions. Part II consists of three chapters, where we focus on the age old problem of nucleation and growth, both from the perspective of thermodynamics and kinetics. We account for the rich history of the problem in the introductory Chapter II.1. In this chapter we describe various types and examples of the nucleation phenomena, and a brief account of the major theoretical approaches used so far. We begin with the most successful Classical Nucleation Theory (CNT), and then move on to more recent applications of Density Functional Theory (DFT) and other mean-field types of models. We conclude with a comparison between the experiments, theories and computational studies. In the next chapter (Chapter II.2) we attempt to elucidate the mechanism of nucleation near the gas-liquid spinodal from a microscopic point of view. Here we construct a multidimensional free energy surface of nucleation of the liquid phase from the parent supercooled and supersaturated vapor phase near the gas-liquid spinodal. In particular, we remove the Becker-Doring constraint of having only one growing cluster in the system. The free energy, as a function of the size of the largest cluster, develops a pronounced minimum at a subcritical cluster size close to the spinodal. This signifies a two step nature of the process of nucleation, where the rapid formation of subcritical nuclei is followed by further growth by slower density fluctuations on an uphill free energy surface. An alternative free energy pathway involving the participation of many subcritical clusters is envisaged near the spinodal where the growth of the nucleus is found to be promoted by a coalescence mechanism in contrast to the single particle addition assumption within CNT. The growth of the stable phase becomes progressively collective and spatially diffuse, and the significance of a “critical nucleus” is lost for deeper quenches. In this chapter we present our studies both in 3dimensional Lennard-Jones (LJ) system and Ising model (both 2and 3dimensions). Our general findings seem to be independent of the model chosen. While the previous chapter focuses on relatively well-studied 3-dimensional (3D) LJ system, in Chapter II.3 we present our studies on the characteristics of the nucleation phenomena in 2dimensional (2D) Lennard-Jones fluid. To the best of our knowledge this is the first extensive computer simulation study to check the accuracy of CNT in 2D. Using various Monte Carlo methods, we calculate the free energy barrier for nucleation, line tension, and bulk densities of equilibrium liquid and vapor phases, and also investigate the size and shape of the critical nucleus. The study is carried out at an intermediate level of supersaturation (away from the spinoidal limit). In 2D, a surprisingly large cutoff (rc ≥ 7.0σ where σ is the diameter of LJ particles) in the truncation of the LJ potential is required to obtain converged results. A lower cutoff leads to a substantial error in the values of the line tension, nucleation barrier, and characteristics of the critical cluster. Note that typically 2.5σ is sufficient for 3D LJ fluids. We observe that in 2D system CNT fails to provide a reliable estimate of the free energy barrier. While it is known to slightly overestimate the nucleation barrier in 3D, it underestimates the barrier by as much as 50% at the saturation ratio S = 1.1(defined as S = P/Pc, where Pc is the coexistence pressure) and at the reduced temperature T* = 0.427(defined as T* = KBT/ ε, where ε is the depth of the potential well). The reason for the marked inadequacy of the CNT in 2D can be attributed to the non-circular nature of the critical clusters. Although the shape becomes increasingly circular and the clusters become more compact with increase in cutoff radius, an appreciable non-circular nature remains even without any cutoff to make the simple CNT inaccurate. Part III again consists of three chapters and focuses on the conformational equilibria. Collapse transition and self-organized structures of n-alkanes in solution. In Chapter III.1 we carry out a brief survey of the existing theories of polymer in solution, with particular emphasis on the collapse process in poor solvents. We also introduce the concept of “hydrophobicity” and “hydrophobic collapse”, which is now a subject enormous interest, partly because it my help in understanding the initial processes involved in protein folding. We briefly discuss the subject of formation of beautiful self-organized structures by block copolymers, and also simple homopolymers which is essentially the focus of the work embodied in the next two chapters. In Chapter III.2 we demonstrated a chain length dependent crossover in the structural properties of linear hydrocarbon (n-alkane) chains using detailed atomistic simulations in explicit water. We identify a number of exotic structures o the polymer chain through energy minimization of representative snapshots collected from molecular dynamics trajectory. While the collapsed state is ring-like(circular) for small chains(CnH2n+2; n ≤ 20) and spherical for very long ones( n = 100), we find the emergence of ordered helical structures at intermediate lengths (n ~ 40). We find different types of disordered helices and toroid-like structures at n = 60. We also report a sharp transition in the stability of the collapsed state as a function of the chain length through relevant free energy calculations. While the collapsed state is only marginally metastable for C20H42, a clear bistable free energy surface emerges only when the chain is about 30 monomers long. For n = 30, the polymer exhibits an intermittent oscillation(characterized by well-developed 1/f noise, where f is the frequency ) between the collapsed and the coil structures, characteristic of two stable states separated by a small barrier. This appears to support a weakly first order phase transition between the extended and the collapsed states. Chapter III.3 extends the study of previous chapter to much longer chains (n ≥ 100), which irreversibly collapse in water into globular forms. Even though the collapsed form has a nearly spherical shape, close inspection shows a propensity towards local ordering in the alignment of the polymer segments. This tendency to maintain alignment in order to maximize the number of contacts leads to a core-shell like structure, where the shell is often characterized by a bent rod-like shape consisting of two adjacent segments running in parallel. A key event associated with the initial stage of collapse seems to be the formation of a skewed ring (or loop) that serves as a “nucleation center” for rest of the chain to collapse into. Time evolution of the radial distribution function of water surrounding the polymer, shows that the density of neighboring water decreases by only about 15-20% from that of bulk water. Even though interior of the ting-like structures is fully devoid of water, solvent accessible surface representation shows that these regions are geometrically/spatially inaccessible to water molecules. We suggest that the role of water is to stabilize such ring-like structures once formed by natural conformational fluctuations of the polymer chain. This view is confirmed by observation of spontaneous formation and melting away of such ring-like entities in a polar aprotic solvent(DMSO). We also comment on the role of the flexibility of polymer chains in determining the collapse kinetics. The last part(Part IV) of the thesis consists of two chapters that deal with the crystallization of linear polymer chains from dilute solution. The way long chain polymers crystallize is drastically different from their small molecule counterparts due to their topological connectivity. Linear polymers often crystallize from dilute solution in the form of thin lamellae with well-defined crystallographic features. In Chapter IV.1 we briefly survey the current theoretical understanding and confusions associated with the highly debated field of polymer crystallization. While the last few decades have seen the development of many successful phenomenological theories, the molecular mechanism of formation of such self-organized lamellae is extremely complex and very poorly understood. There are clearly two distinct steps in polymer crystallization. Firstly, the individual linear polymers must self-organize into bundles of somewhat regular structures. These structures then further aggregate to lamellar form and crystallize into a lattice. In this respect , it has marked similarity to the problem of protein crystallization. In chapter IV.2 we present Brownian dynamics simulation studies of a single polythelene chain of length 500. Such systems can reasonably mimic the process of crystallization from dilute solutions. Our simulations could successfully reproduce some of the interesting phenomena observed in experiments and very recent computer simulation studies, including multi-center nucleation of rod-like structures within a single polymer chain, an inverse relation between lamellar thickness and temperature etc. But our primary focus has been to understand the nature of the phase transition as one traverses along the melting temperature and the underlying free energy surface. Near the melting temperature we observe a very intriguing fluctuation between the disordered molten globule state and the ordered rod-like crystalline, where these two forms have highly different shape and structure. These fluctuations have strong signature of 1/f noise or intermittency. This clearly indicates the existence of a weakly first order transition, where two widely different states with large difference in values of order parameter are separated by a rather small free energy barrier. This can be related to the experimentally observed density fluctuations that resemble spinodal decomposition. It is important to note that very similar fluctuations have been observed in our previous studies on liquid crystals (Chapter 1.2) and intermediate sized alkalines in water(Chapter III.2) that signifies a universal underlying energy landscape for these systems. We have discussed the scope of future work at the end of each chapter whenever appropriate.

This thesis reports light-scattering experiments and visual investigations close to the critical point, in the solvophobic systems, 3-methylpyridine (3MP) + heavy water (D2O) + sodium bromide (NaBr) and methyl ethyl ketone (MEK) + water (W) + secondary butyl alcohol (sBA). The system 3MP + D2O + NaBr was chosen in order to throw more light on the reported crossover from mean-field to Ising-type of critical behaviour shown by this system and to investigate the existence of a mean-field tricritical point in it at an NaBr weight fraction of X = 0.1700, two issues that have been the subject of an intense scientific debate in recent years. The system MEK + W + sBA is the result of our search for a system, other than, the well known 3-methylpyridine (3MP) + water (W) + heavy water (HW) + potassium iodide (KI), in which a quadruple critical point (QCP) can potentially be realized. In addition to this the thesis provides exhaustive details regarding the design, fabrication, and characterization, of a microkelvin thermostat in which a temperature stability of the order of a few microkelvin is achievable despite its relatively simple thermal design. The thesis is organized into 6 Chapters. Chapter 1 provides an introduction to the field of critical phenomena in liquid mixtures. The critical phenomena observed in various systems such as simple fluids, ionic fluids, polymer blends and polymer solutions, and micellar and microemulsion systems, are discussed in brief. Particular attention has been paid to the investigations by various researchers, into, the crossover from Ising to mean-field critical behaviour in electrolyte and polymer solutions, and in amphiphilic systems. Recent theoretical attempts at modeling ionic criticality have also been cited and summarized. A brief discussion on the various types of special critical points and multicritical points that are observed in multicomponent liquid mixtures and other condensed matter systems has been provided. The appealing possiblity of the presence of multicritical points in ionic fluids leading to crossover behaviour is also discussed. The chapter ends with a statement on the goals of this thesis. Chapter 2 describes the instrumentation and other aspects of the experimental techniques used for the light-scattering studies reported in this thesis. Details about the thermal instrumentation such as the water bath and the silicone-oil bath used for the visual investigation experiments and the metal thermostat used for the light-scattering experiments have been provided. The important design considerations relating to the achievement of a high degree of temperature stability (Formula) have been elucidated clearly. The modifications made to the design of the light-scattering thermostat, that enables achievement of a temperature stability of ± 2.5 mK at temperatures 19 ≤ T ≤ 24°C has been discussed. A section has been devoted to the description of the calibration of the temperature sensors we used in our experiments. The light-scattering instrumentation has been discussed in depth. The difficulties associated with the light-scattering techniques when it is used as a tool to study critical phenomena have been detailed. This is followed by a description of the method we used in correcting our light-scattering data for double-scattering effects. A description of the sample cells used for visual investigations and light-scattering experiments along with the sample filling and cleaning procedures followed by us has been described. Chapter 3 deals with the first of the three important problems discussed in this thesis. The chapter is aimed at investigating the crossover behaviour of the solvo-phobic system 3-methylpyridine (3MP)+ water (H2O) + sodium bromide (NaBr), by means of light-scattering studies on the strongly motivated and non-trivial system of 3-methylpyridine (3MP) + heavywater (D2O) + sodium bromide (NaBr). The replacement of H2O by D2O in 3MP + D2O + NaBr, is expected to accentuate the crossover behaviour reportedly displayed by 3MP + H2O + NaBr, and thereby, provide conclusive evidence regarding the existence or otherwise of a crossover between the Ising- and the mean-field-types of critical behaviour in this system. The chapter begins with a detailed literature survey on the topic of the crossover behaviour shown by the system 3MP + H2O + NaBr. We also provide a survey of the effect of the iso-topic H→D substitution on the critical behaviour of binary and quasibinary systems. Through an argument based on small-angle neutron scattering (SANS) studies and the Kirkwood-Buff integrals (KBIs), a strong and cogent motivation is established, which proves that, if the reported crossover behaviour in 3MP + H2O + NaBr is assumed to be correct, then the system 3MP + D2O + NaBr should display not just the same crossover behaviour as shown by the undeuterated system 3MP + H2O + NaBr, but, in addition, also a more pronounced dependence of the crossover temperature on the concentration of NaBr in the mixture than that seen in 3MP + H2O + NaBr. This approach to understand the crossover behaviour of 3MP + H2O + NaBr, has not been used by any of the previous investigators. The coexistence curve data for the system 3MP + D2O + NaBr are obtained at six different values of the NaBr weight fractions viz. X = 0, 0.0250, 0.0800, 0.1200, 0.1500, and 0.1800. The closed-loop immiscibility loop obtained for X = 0, agrees well with the reported phase diagram for 3MP + D2O in the literature. A comparison between the lower-critical lines obtained for the deuterated and the undeuterated system has been provided. Within error bars, no perceptible dip was observed in the critical line at X = 0.1700 in the case of the system 3MP + D2O + NaBr. Hence, our study does not indicate the presence of a mean-field tricritical point that has been reported at X = 0.1700 in the system 3MP + H2O + NaBr. A large section of Chapter 3 is devoted to the results and discussions of our extensive light-scattering experiments on the system 3MP + D2O + NaBr. The experiments were performed on 13 different samples of 3MP + D2O + NaBr with NaBr weight fractions in the range of 0 ≤ X ≤ 0.1900. The choice of the X values were guided by the NaBr concentrations at which earlier investigators have done light-scattering experiments on the system 3MP + H2O + NaBr. Detailed light-scattering experiments reveal that the system 3MP + D2O + NaBr shows a simple Ising-type critical behaviour with γ ' 1.24 and ν ' 0.63 over the entire NaBr concentration range 0 ≤ X ≤ 0.1900. The crossover behaviour is predominantly nonmonotonic, and the crossover is completed well outside the critical domain. An analysis in terms of the effective susceptibility exponent (γeff) showed that the crossover behaviour is nonmonotonic for 0 ≤ X ≤ 0.1793 and tends to become monotonic for X > 0.1793. The correlation length amplitude, ξo, has a value of (Formula) for 0.0250 < X ≤ 0.1900, whereas for (Formula). Since isotopic H—> D substitution is not expected to change the critical behaviour of the system, our results shows that the system 3MP + H2O + NaBr should exhibit universal Ising-type critical behaviour that is typical for aqueous solutions. Our search for a new system in which a quadruple critical point (QCP) could possibly be realized forms the subject matter of the Chapter 4 of the thesis. The system methyl ethyl ketone (MEK) + water (W) + secondary butyl alcohol (sBA) is identified as a very promising candidate-system for this purpose. The chapter begins with a brief survey of the various types of multicritical points and special critical points realizable in multicomponent liquid mixtures. The importance of investigating special critical points such as the QCP is motivated. A detailed coexistence surface for MEK + W + sBA was developed by generating the coexistence curves corresponding to five different, but onstant, values of MEK weight fractions XM = 0.0500, 0.1000, 0.1750, 0.2300, and 0.3000, respectively. The complete isobaric coexistence surface (at 1 atm) for the system MEK + W + sBA was visualized in the form of a prismatic phase diagram. The surface is found to display a tunnel-like appearance in the MEK weight fraction range of 0.0500 ≤ XM ≤ 0.1750, with the tunnel being the narrowest at the point (XM,XW,XSBA) = (0.1750, 0.5801, 0.2449), where, xw and XSBA are, respectively, the weight fractions of water and sBA in the mixture. An analysis of the order parameter data showed that MEK + W + sBA shows near Ising-type of critical behaviour near their upper critical solution temperatures, TU's. It was seen that the critical temperature Tc shows a low drift with time (Formula)/day and that the tunnel-like portion in the phase diagram of MEK + W + sBA was very symmetric. These two features make (MEK + W + sBA) a considerably more promising system than (3MP + W + HW + KI )for the realization of the QCP. It may be recalled that 3MP + W + HW + KI is the only system in which QCP studies have been reported so far in literature. The light-scattering investigations in MEK + W + sBA near the lower critical solution temperatures TL are described next. We corrected our light-scattering data for both turbidity as well as double-scattering effects. Our experiments revealed that (MEK + W + sBA) shows near three-dimensional-Ising type of critical behaviour at the lower critical solution temperatures, with the susceptibility exponent (γ) in the range of 1.217 ≤ γ ≤ 1.246. The correlation length amplitudes (ξo) and the critical exponent (ν) of the correlation length (ξ) were in the ranges of 3.536 ≤ ξo ≤ 4.611 A and 0.619 ≤ ν ≤ 0.633, respectively. An analysis in terms of the effective susceptibility exponent (γeff) results in the interesting result, namely that, the critical behaviour of (MEK + W + sBA ) is of the Ising-type for MEK concentrations in the ranges of 0.1000 ≤ XM ≤ 0.1250 and XM ≥ 0.3000; but, for the intermediate range of 0.1750 < XM < 0.3000, the system shows a tendency towards mean-field type of critical behaviour. This behaviour is interesting because both the constituent binary systems of the ternary system (MEK + W + sBA), namely, (MEK + W) and (W + sBA) show Ising-type of critical behaviour. Chapter 5 discusses another crucial objective of this thesis, namely, the fabrication and characterization of a microkelvin thermostat, which has been built for the purpose of performing light-scattering studies exceptionally close to the critical temperature. At the outset, the need for a temperature stability of the order of a few microkelvin for performing reliable critical point phenomena experiments very close to the critical point, is justified and demonstrated. This is followed by an in-depth account of the thermal design of the thermostat and the electronic circuitry used in the temperature controller. The variations in the ambient temperature and the stability of the bridge excitation source are identified and demonstrated to be crucial factors that affect the long-term temperature stability of the thermostat. A simple compensation scheme to nullify the effects of ambient temprature variations on the controller performance is suggested. It is demonstrated that the thermostat gives a temperature stability of (Formula) and ±60−90 µK for 7 − 14 h over a broad range of 25 − 103 °C. A detailed profile of thermal gradients within the sample recess is provided. It is shown that the parameter ∆Teff [i.e., the difference between the maximum (minimum if ∆Teff has a negative value) temperature within the sample recess and the temperature just outside the sample recess] is a more relevant parameter than ∆T (i.e., the temperature difference between the inner and the outer stages) in understanding the behaviour of multistage thermostats. The most important result that emerges from our study is that the thermal gradients and the transient response of the controller, can both be tuned by varying ∆Teff (or by varying ∆T). The best horizontal and vertical thermal gradient performance observed within our thermostat were 250 and 100 µK/mm, respectively, which are observed for a ∆Teff = 4.46 mK. The transient response of the controller is almost invariant for ∆Teff > 0 but it shows a dramatic decrease of almost 50% when ∆Teff < 0. It is seen that, the limit ∆Teff →>• 0, provides the best operating conditions of the thermostat from the standpoints of temperature stability, transient response and gradient performance. An error analysis relevant to the circuitry used by us is provided at the end of the chapter, which clearly indicates the efficacy of the compensations scheme proposed by us to nullify the effects of ambient temperature variations. Chapter 6 summarizes the important results obtained in this thesis. It also presents a range of open problems that need to be explored further in order to fully understand the results that are reported in this thesis, especially, regarding the type of crossover behaviour seen in the systems 3MP + D2O + NaBr and MEK + W + sBA.

Transition metal and related compounds have been extensively studied over the past several decades. These investigations revealed a wide range of behavior, encompassing colossal magnetoresistance (CMR), high-TC superconductivity, and magnetic semiconductivity, all of which continue to present fundamental challenges to the understanding of such phenomena. There is, however, a close correlation between such characteristics and the appearance of magnetic order. This correlation underlies the present study, which focuses on the magnetic and transport behavior of various Manganese (Mn), Iron (Fe) and Cobalt (Co) containing materials, with particular emphasis on the nature of the magnetic order they display and the critical exponents that characterize the accompanying phase transition. The magnetic and transport properties of two specific systems will be covered: first various doped manganites from the series (La,Pr)1-x(Ca,Ba)xMnO3, and second the magnetic semiconductors Fe0.8Co0.2Si and Ga0.98Mn0.02As. In the manganites, the influence of doping on; (i) the evolution of the metal-insulator transition (MIT) with composition; (ii) the universality class of the magnetic critical behavior associated with the paramagnetic to ferromagnetic transition, which occurs in the vicinity of a MIT with which CMR is associated; (iii) the mechanisms underlying ferromagnetism across the MIT; (iv) the correlation between the appearance of a Griffiths-like phase and CMR, and (v) the origin of Griffiths-like phase have been investigated. Four different systems have been studied: La1-xCaxMnO3 (0.18 ≤ x ≤ 0.27), La1-xBaxMnO3 (x ≤ 0.33), (La1-yPry)0.7Ca0.3Mn16/18O3 (y ≤ 0.85), and Pr1-xCaxMnO3 (x = 0.27, 0.29). In Fe0.8Co0.2Si and Ga0.98Mn0.02As, the scaling between magnetization and conductivity has been the subject of ongoing debate. In bulk Fe0.8Co0.2Si, a novel scaling between the anomalous Hall effect (AHE) and the magnetization enables the anomalous Hall coefficient to be accurately determined. In turn, this enables the universality class for the transition to ferromagnetism to be established independently from the anomalous Hall conductivity. In an epitaxial (metallic) Ga0.98Mn0.02As microstructure, the magnetization has been indirectly determined from the AHE. Subsequent analysis yields magnetic critical exponents consistent with the Mean-Field model, direct support for which had previously been lacking.

Transition metal and related compounds have been extensively studied over the past several decades. These investigations revealed a wide range of behavior, encompassing colossal magnetoresistance (CMR), high-TC superconductivity, and magnetic semiconductivity, all of which continue to present fundamental challenges to the understanding of such phenomena. There is, however, a close correlation between such characteristics and the appearance of magnetic order. This correlation underlies the present study, which focuses on the magnetic and transport behavior of various Manganese (Mn), Iron (Fe) and Cobalt (Co) containing materials, with particular emphasis on the nature of the magnetic order they display and the critical exponents that characterize the accompanying phase transition. The magnetic and transport properties of two specific systems will be covered: first various doped manganites from the series (La,Pr)1-x(Ca,Ba)xMnO3, and second the magnetic semiconductors Fe0.8Co0.2Si and Ga0.98Mn0.02As. In the manganites, the influence of doping on; (i) the evolution of the metal-insulator transition (MIT) with composition; (ii) the universality class of the magnetic critical behavior associated with the paramagnetic to ferromagnetic transition, which occurs in the vicinity of a MIT with which CMR is associated; (iii) the mechanisms underlying ferromagnetism across the MIT; (iv) the correlation between the appearance of a Griffiths-like phase and CMR, and (v) the origin of Griffiths-like phase have been investigated. Four different systems have been studied: La1-xCaxMnO3 (0.18 ≤ x ≤ 0.27), La1-xBaxMnO3 (x ≤ 0.33), (La1-yPry)0.7Ca0.3Mn16/18O3 (y ≤ 0.85), and Pr1-xCaxMnO3 (x = 0.27, 0.29). In Fe0.8Co0.2Si and Ga0.98Mn0.02As, the scaling between magnetization and conductivity has been the subject of ongoing debate. In bulk Fe0.8Co0.2Si, a novel scaling between the anomalous Hall effect (AHE) and the magnetization enables the anomalous Hall coefficient to be accurately determined. In turn, this enables the universality class for the transition to ferromagnetism to be established independently from the anomalous Hall conductivity. In an epitaxial (metallic) Ga0.98Mn0.02As microstructure, the magnetization has been indirectly determined from the AHE. Subsequent analysis yields magnetic critical exponents consistent with the Mean-Field model, direct support for which had previously been lacking.

A presente pesquisa se refere à aplicação dos métodos estocásticos para estudar fenômenos críticos em modelos de sistemas classificados como desordenados que apresentam transição de fase do tipo-ordem desordem. Essa pesquisa é definida tanto no quadro teórico da Mecânica Estatística dos fenômenos críticos e transição de fase de equilíbrio e fora de equilibrio, com os recursos associados à análise de escala de tamanho finito quanto no quadro dos recursos aos processos estocásticos markovianos, descritos pela equação-mestra e associados a técnicas essencialmente numéricas como o método estocástico computacional de Monte Carlo. Na primeira etapa desta pesquisa, os modelos estudados são da classe denominada de votante majoritário. Eles são indexados pelo número z de vizinhos mais próximos com spin central, tem dois estados e são construidos em redes quadradas. A evolução dinâmica é dada pela regra da maioria junto com regradfe desempate. Eles não satisfazem a propriedade do principio do balanceamento detalhado, portanto, são classificados como descrevendo fenômenos fora do equilíbrio. Contudo, eles satisfazem a propriedade de simetria de inversão de sinal, o que os coloca teoricamente na classe de universalidade do modelo de Ising. Desta forma, a evolução dinâmica desses modelos é estudada com os recursos da equação mestra ou equação de evolução. No entanto, essa abordagem teórica é feita apenas na aproximação de campo médio, a qual fornece, na solução estacionária, os valores clássicos para os parametros relevantes. Em contrapartida, os valores numéricos exatos para os valores do ponto crítico e dos expoentes críticos, que são não clássicos, é dada por meio do recurso ao método de simulação computacional e à análise de escala de tamanho finito. Esses valores confirmam o resultado teórico quanto à classe de universalidade para cada modelo específico. Na sequência, estudam-se as propriedades dos modelos resultantes da combinação convexa do votante majoritário. Os resultados são semelhantes aos anteriores. Um resultado extra permitido por essas combinações convexa éa construção de uma relação contínua entre o valor crítico indutor da transição de fase e o número de vizinhos. Neste contexto foi apresentada uma solução para o problema do modelo mais simples desta classe de modelos. Com o modelo mais simples ilustram-se as condições universais de transição de fase, em particular o papel da dimensão do sistema. Na segunda etapa da pesquisa, cvonstrí-se, então, outra classe de modelos do votante que, por analogia com o modelo de Ising, tem como estado fundamental a fasse antiferromagnética: a classe dos modelos do votante minoritário. Essa classe de modelos possue as mesmas propriedades da classe de modelos do votante majoritário e por isso obtem-se os mesmos resultados. A analogia com o modelo de Ising é levada um pouco mais longe com a construção de um análogo aos modelo +-J: a construção da combinação convexa do votante majoritário com o minoritário. Para esse novo modelo constrói-se tanto o diagrama com as três fases, ferromagnética, paramagnética e antiferromagnética quanto as concentrações críticas que as distinguem. Não se obtém uma possível fase de vidro de spin. Uma vez que os modelos do votante são originalmente tidos como sistemas desordenados, comparam-se, para um mesmo modelo, resultados obtidos pela aplicação de dois diferentes métodos de tratar os modelos de sistemas desordenados: o método temperado-\"quenched\" - e o método recozido - \"annealed\". Na terceira etapa desta pesquisa e na mesma linha dos modelos estocásticos irreversíveis tratados anteriormente, estuda-se ainda outro modelo, classificado como jogo espacial nos sítios de uma rede quadrada. Simulações mostram que além de dois estados absorventes ha\'também a presença de um estado ativo definido por uma densidade finita de cooperadores e não cooperadores e que esse modelo se encontra na classe de universalidade do modelo de percolação direcionada. Nesta mesma etapa, mas, agora, no contexto da Mecânica sStatística de Equilíbrio, aborda-se o modelo de Ising quântico unidimensional com campo transverso por meio de simulação de Monte Carlo.Com o uso do método estiocástico e por meio da curva do colapso calculam-se os valores do ponto crítico e dos expoentes críticos desse modelo. / This research refers to the applications of the stochastic methods to the study of the critical phenomena in models of systems classified as disordered that undergo phase transition of the order-disorder kind. This research is defined as in the theoretical framework of the Statistical mechanics of the equilibrium and non-equilibrium of the critical phenomena and phase transition with the resources associated to the analysis of finite-size scale, as in the frame of the resources of markovian stochastic process described by the master equation associated with essentially numerical techniques such as stochastic computational method of Monte Carlo.l In this first stage of this research, the studied models belong to the class of the majority voter. They are described by a lattice with spins in each site with two states. The dynamic of these models is described by the majority rule together with a rule for solving problems of indecision. These models do not obey the principle of microscopic reversibility therefore they are classified as describing phenomena of non-equilibrium. However, they satisfy the property of \"up-down\" symmetry which make theoretically belong to the universality class of the Ising model. The mean field approach to the master equation is done and the exact value is pursued by the use of the method of the computational simulation with theuse of the analysis of finite-size scale. The results obtained for the critical exponents support the hypothesis of universality class of these models. There are constructions of the convex combination of these models. A question is raised about the simplest model and a possible solution is presented. There is a search for another kind of majority voter, but with an antiferromagnetic ground state, which leads to the minority voter. It is also to be classified in the same universality class. A natural unfold of this research is making the convex combination of the minority and majority voter models by analogy with the Ising model +- J and ask for the phase diagram class.Some results are also obtained by comparing the quenched and annealed approach to a same majority voter model. Finally, there are two more applications of these methods for obtaining critical point and critical exponents. The first refers to a model with absorbing state which is classified in the universality class of direct percolation. The second refers to a quantum model with transverse field.

Investigações da dinâmica crítica em modelos de magnetismo, para tempos curtos, têm aparecido com grande freqüência na literatura. Essa técnica foi descoberta por Li, Schülke e Zheng que, inspirados em trabalhos anteriores de Huse e Janssen et al., mostraram que generalizações de grandezas como a magnetização e o cumulante de Binder exibem comportamento universal já no início da simulação. O estudo da criticalidade em tempos curtos proporciona um caminho alternativo para a estimativa do expoente z, além de permitir o cálculo de um novo expoente dinâmico &#952;, associado ao comportamento anômalo da magnetização. Da mesma forma, simulações dependentes do tempo tornaram-se ferramenta útil para estudar transições de fase em autômatos celulares e modelos de spin. Em particular, as melhores estimativas para o expoente z do Ising bidimensional foram obtidas por meio da técnica de propagação de danos, introduzida por Kauffman no estudo de autômatos e mais tarde generalizada para modelos de spin. Na primeira parte deste trabalho utilizamos o método Monte Carlo em tempos curtos para investigar o modelo de Baxter-Wu, definido em uma rede bidimensional triangular com variáveis do tipo Ising, acopladas por interações de três corpos. Obtivemos os expoentes críticos dinâmicos z e &#952; além dos índices críticos estáticos ß e Nû. Os resultados não corroboram aqueles recentemente obtidos por Santos e Figueiredo para o expoente z. Na segunda parte do trabalho, investigamos a propagação de danos no modelo de Ising unidimensional submetido a duas dinâmicas propostas por Hinrichsen e Domany (HD). Em particular, nós estudamos o efeito da atualização síncrona (paralela) e assíncrona (dinâmica contínua) sobre o espalhamento do dano. Mostramos que o dano não se propaga quando a segunda dinâmica é implementada de forma assíncrona. Também mostramos que as regras para atualização do dano produzidas por essa dinâmica, quando a temperatura vai a infinito e um certo parâmetro Lambda é igual a zero, são equivalentes àquelas do bem conhecido autômato celular (modelo A) de Grassberger. / Short-time simulations have been used with great frequency in the literature. That technique was discovered by Li, Shülke and Zheng that, inspired in previous works by Huse and Janssen et al., showed that generalizations of quantities like magnetization and the Binder´s cumulant exhibit universal behavior in the beginning of the simulation (early time behavior). The study of criticality in short-times provides an alternative way to estimate the dynamic critical exponent z, besides allowing the calculation of a new dynamic exponent &#952;, associated to the anomalous behavior of the magnetization. In the same way, time-dependent simulations became a useful tool to study phase transitions in cellular automata and also for spin models. In fact, the best estimates for the exponent z of the two-dimensional Ising model were obtained through the technique of damage spreading, introduced by Kauffman in the study of cellular automata, later widespread for spin models. In the first part of this work we used short-time Monte Carlo simulations to investigate the Baxter-Wu model, defined in a triangular lattice whose variables are Ising-like coupled by triplet interactions. We have obtained estimates for the dynamic critical exponents z and &#952; besides static exponents ß e Nû. Our results do not corroborate recent estimates by Santos and Figueiredo for the critical exponent z. In the second part of this work, we investigated the damage spreading in the one-dimensional Ising model under two dynamics introduced by Hinrichsen and Domany (HD). In particular, we study the effects of synchronous (parallel) and asynchronous (continuous dynamics) updating on the spreading properties. We showed that the damage does not spread when the second dynamic is implemented in an asynchronous way. We found that the rules for updating the damage produced by this dynamic, as the temperature goes to infinity and a certain parameter Lambda is zero, are equivalent to those of Grassberger’s well-known model A cellular automaton.

Neste trabalho, nós investigamos o comportamento crítico dinâmico de três modelos estatísticos utilizando simulações Monte Carlo em tempos curtos. Inicialmente, estudamos os modelos tridimensionais de dupla-troca e de Heisenberg. O expoente dinâmico de persistência global, bem como o expoente z são estimados através de duas técnicas. Para obter o expoente de persistência global, aplicamos diretamente a lei de potência obtida para a probabilidade de persistência global e em seguida fizemos o colapso de uma função universal para duas redes de tamanhos diferentes. Para estimar o valor de z, nós usamos uma função mista que combina resultados de simulações realizadas com diferentes condições iniciais e o cumulante de Binder de quarta ordem dependente do tempo. O expoente dinâmico que governa o comportamento tipo lei de potência da magnetização inicial, é estimado através da correlação temporal da magnetização (modelos de dupla-troca e Heisenberg) e da aplicação direta de uma lei de potência (modelo de Heisenberg). Os expoentes estáticos da magnetização e comprimento de correlação são estimados seguindo o comportamento de escala do parâmetro de ordem e sua derivada, respectivamente. Os resultados confirmam que esses dois modelos pertencem à mesma classe de universalidade. Em seguida, alguns expoentes críticos dinâmicos e estáticos são estimados no ponto de bifurcação do modelo de spin com simetria Z(5) bidimensional. Neste ponto, o modelo apresenta dois parâmetros de ordem diferentes, cada um possuindo um conjunto diferente de índices críticos. Os valores dos expoentes críticos estáticos estão em boa concordância com os resultados exatos. Até onde sabemos, está é a primeira tentativa de se obter os expoentes críticos dinâmicos para os modelos de dupla troca, Heisenberg e para o modelo Z(5). / In this work, we investigate the dynamic critical behavior of three statistical models by using short-time Monte Carlo simulations. At first, we study the three-dimensional double-exchange and Heisenberg models. The global persistence exponent, as well as the exponent z are estimated through two techniques. The dynamical exponent of global persistence is obtained by using the straight application of the power law obtained for the global persistence probability and by following the scaling collapse of a universal function for two diferent lattice sizes. To estimate the value of z, we use a mixed function which combines results obtained from samples submitted to diferent initial configurations and the time dependent fourth-order Binder cumulant. The dynamical exponent which governs the power law behavior of the initial magnetization, is estimated through the time correlation of the magnetization (double-exchange and Heisenberg models) and through the straight application of a power law(Heisenberg model). The statical exponents of the magnetization and correlation length are estimated through the scaling behavior of the order parameter and its derivative, respectively. The results confirm which those models belong to the same universality class. Following, the dynamical exponents and the statical exponents are estimated at the bifurcation point of the two-dimensional Z(5)-symmetric spin model. In this point, the model presents two diferent order parameters, each one possessing a diferent set of critical indices. The values of the static critical exponents are in good agreement with the exact results. Our study is, to the best of our knowledge, the first attempt to obtain the dynamic critical exponents of the double-exchange, Heisenberg, and Z(5) models.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2018-09-12T10:47:41Z No. of bitstreams: 2 Dissertação - Airton Modesto da Cunha - 2018.pdf: 36005906 bytes, checksum: 5f095bd3c548d6f6e958d83f126908ef (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2018-09-12T10:50:15Z (GMT) No. of bitstreams: 2 Dissertação - Airton Modesto da Cunha - 2018.pdf: 36005906 bytes, checksum: 5f095bd3c548d6f6e958d83f126908ef (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2018-09-12T10:50:15Z (GMT). No. of bitstreams: 2 Dissertação - Airton Modesto da Cunha - 2018.pdf: 36005906 bytes, checksum: 5f095bd3c548d6f6e958d83f126908ef (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2018-08-09 / The present dissertation is the result of the educational, “Teaching model of electrical resistors to describe fractures in physical systems”, product worked in a class of the third year of high school of the State School Prof. Marcolino de Barros of the municipality of Patos de Minas-MG. In which, we present a simple pedagogical model with the purpose of studying the complex process of ruptures in physical systems. For this, we developed an experimental model together with its theoretical counterpart where we consider a system of electric resistors network subject to a potential difference and analyze the current that passes through the system as a function of the random removal of their resistive components. We use a circuit board, voltage source stabilized at a pre-established potential difference, and a resistor network with a few ohms units each. After the proposed experiments are executed, we obtained appropriate experimental data and from these graphs are generated with which the dependence of the current through the circuit with the interruption of the joints is shown. Taking into account that this system behaves as an ohmic system, the model is used to study several relevant physical concepts. As is the case of an elastic solid subject to Hooke’s law- like deformations, this is then a very broad model. / A presente dissertação é resultado de nosso produto educacional, “Modelo pedagógico de resistores elétricos para descrever fraturas em sistemas físicos”, trabalhado em uma turma do terceiro ano do ensino médio da Escola Estadual Prof. Marcolino de Barros do município de Patos de Minas-MG. No qual, apresentamos um modelo pedagógico simples com a finalidade de estudar o complexo processo de rupturas em sistemas físicos. Para tanto, desenvolvemos um modelo experimental munido de sua contraparte teórica onde consideramos um sistema de resistores elétricos sujeito a uma diferença de potencial e analisamos a corrente que passa através do sistema em função da remoção aleatória doscomponentes resistivos. Usamos uma placa de circuitos, fonte de tensão estabilizada em uma diferença de potencial pré -estabelecida e uma malha de resistores com algumas unidades de ohms cada. Realizadas as experiências propostas obtivemos apropriados dados experimentais e a partir destes foram gerados gráficos com os quais são mostrados a dependência da corrente através do circuito com a interrupção das junções. Levando em consideração que este sistema se comporta como um sistema ôhmico, o modelo é usado para estudar vários conceitos físicos relevantes. Como é o caso de um solido elástico sujeito a deformações do tipo lei de Hooke, sendo este então um modelo de caráter bem amplo.