[pt] A investigação da geometria quântica em semicondutores e isoladores tornou-se significativa devido às suas implicações nas características dos materiais. A noção de geometria quântica surge considerando a métrica quântica do estado de Bloch da banda de valência, que é definido a partir da sobreposição dos estados de Bloch em momentos ligeiramente diferentes. Ao integrar a métrica quântica em toda a zona de Brillouin, introduzimos uma quantidade que chamamos de número de fidelidade, que significa a distância média entre estados de Bloch adjacentes. Além disso, apresentamos um formalismo para expressar o número de fidelidade como um marcador de fidelidade local no espaço real que pode ser definido em qualquer sítio da rede. O marcador pode ser calculado diretamente diagonalizando o hamiltoniano da rede que descreve o comportamento das partículas na rede. Posteriormente, o conceito de número e marcador de fidelidade é estendido para temperatura finita utilizando a teoria de resposta linear, conectando-os a medições experimentais que envolvem analisar o poder de absorção óptica global e local quando o material é exposto à luz linearmente polarizada. Particularmente para materiais bidimensionais, a opacidade do material permite a determinação direta do número de fidelidade espectral, permitindo a detecção experimental do número de fidelidade. Finalmente, um marcador de fidelidade não local é introduzido considerando a divergência da métrica quântica. Este marcador é postulado como um indicador universal de transições de fase quântica, assumindo que o momento cristalino permanece um número quântico válido. Este marcador não local pode ser interpretado como uma função de correlação dos estados de Wannier, que são funções de onda localizadas que descrevem estados eletrônicos em um cristal. A generalidade e aplicabilidade destes conceitos são demonstradas através da investigação de vários isoladores topológicos e transições de fase topológicas em diferentes dimensões. Essas descobertas elaboram o significado dessas quantidades e sua conexão com vários fenômenos fundamentais na física da matéria condensada. / [en] The investigation of quantum geometry in semiconductors and insulators has become significant due to its implications for material characteristics. The notion of quantum geometry arises by considering the quantum metric of the valence-band Bloch state, which is defined from the overlap of the Bloch states at slightly different momenta. By integrating the quantum metric through-out the Brillouin zone, we introduce a quantity that we call fidelity number, which signifies the average distance between adjacent Bloch states. Furthermore, we present a formalism to express the fidelity number as a local fidelity marker in real space that can be defined on every lattice site. The marker can be calculated directly by diagonalizing the lattice Hamiltonian that describes particle behavior on the lattice. Subsequently, the concept of the fidelity number and marker is extended to finite temperature using linear-response theory, connecting them to experimental measurements which involves analyze the global and local optical absorption power when the material is exposed to linearly polarized light. Particularly for two-dimensional materials, the material s opacity enables straightforward determination of the fidelity number spectral, allowing for experimental detection of the fidelity number. Finally, a nonlocal fidelity marker is introduced by considering the divergence of the quantum metric. This marker is postulated as a universal indicator of quantum phase transitions, assuming the crystalline momentum remains a valid quantum number. This nonlocal marker can be interpreted as a correlation function of Wannier states, which are localized wave functions describing electronic states in a crystal. The generality and applicability of these concepts are demonstrated through the investigation of various topological insulators and topological phase transitions across different dimensions. These findings elaborate the significance of these quantities and their connection to various fundamental phenomena in condensed matter physics.

In the study of strongly interacting condensed-matter systems controlled microscopic theories hold a key position. Spin-wave theory, large-N expansion, and $epsilon$-expansion are some of the few successful cornerstones. In this doctoral thesis work, we have developed a novel large-$d$ expansion method, $d$ being the spatial dimension, to study model Hamiltonians hosting a quantum phase transition between a paramagnet and a magnetically ordered phase. A highlight of this technique is that it can consistently describe the entire phase diagram of the above mentioned models, including the quantum critical point. Note that most analytical techniques either efficiently describe only one of the phases or suffer from divergences near the critical point. The idea of large-$d$ formalism is that in this limit, non-local fluctuations become unimportant and that a suitable product state delivers exact expectation values for local observables, with corrections being suppressed in powers of $1/d$. It turns out that, due to momentum summation properties of the interaction structure factor, all diagrams are suppressed in powers of $1/d$ leading to an analytic expansion. We have demonstrated this method in two important systems namely, the coupled-dimer magnets and the transverse-field Ising model. Coupled-dimer magnets are Heisenberg spin systems with two spins, coupled by intra-dimer antiferromagnetic interaction, per crystallographic unit cell (dimer). In turn, spins from neighboring dimers interact via some inter-dimer interaction. A quantum paramagnet is realized for a dominant intra-dimer interaction, while a magnetically ordered phase exists for a dominant (or of the same order as intra-dimer interaction) inter-dimer interaction. These two phases are connected by a quantum phase transition, which is in the Heisenberg O(3) universality class. Microscopic analytical theories to study such systems have been restricted to either only one of the phases or involve uncontrolled approximations. Using a non-linear bond-operator theory for spins with S=$1/2$, we have calculated the $1/d$ expansion of static and dynamic observables for coupled dimers on a hypercubic lattice at zero temperature. Analyticity of the $1/d$ expansion, even at the critical point, is ensured by correctly identifying suitable observables using the mean-field critical exponents. This method yields gapless excitation modes in the continuous symmetry broken phase, as required by Goldstone\'s theorem. In appropriate limits, our results match with perturbation expansion in small ratio of inter-dimer and intra-dimer coupling, performed using continuous unitary transformations, as well as the spin-wave theory for spin-$1/2$ in arbitrary dimensions. We also discuss the Brueckner approach, which relies on small quasiparticle density, and derive the same $1/d$ expansion for the dispersion relation in the disordered phase. Another success of our work is in describing the amplitude (Higgs) mode in coupled-dimer magnets. Our novel method establishes the popular bond-operator theory as a controlled approach. In $d=2$, the results from our calculations are in qualitative agreement with the quantum Monte Carlo study of the square-lattice bilayer Heisenberg AF spin-$1/2$ model. In particular, our results are useful to identify the amplitude (Higgs) mode in the QMC data. The ideas of large-$d$ are also successfully applied to the transverse-field Ising model on a hypercubic lattice. Similar to bond operators, we have introduced auxiliary Bosonsic operators to set up our method in this case. We have also discussed briefly the bilayer Kitaev model, constructed by antiferromagnetically coupling two layers of the Kitaev model on a honeycomb lattice. In this case, we investigate the dimer quantum paramagnetic phase, realized in the strong inter-layer coupling limit. Using bond-operator theory, we calculate the mode dispersion in this phase, within the harmonic approximation. We also conjecture a zero-temperature phase diagram for this model.

Thesis (PhD)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: Low-dimensional materials are known to undergo phase transitions to differently or- dered states, when cooled to lower temperatures. These phases often show a periodic modulation of the charge density (called a charge density wave – CDW) coupled with a periodic perturbation of the crystal lattice (called a periodic lattice distortion – PLD). Although many experiments have been performed and much has been learnt about CDW phases in low-dimensional materials, the reasons for their existence are still not fully understood yet. Many processes, involving either strong electron–electron or electron–lattice coupling, have been observed which all might play a role in explaining the formation of different phases under different conditions. With the availability of femtosecond lasers it has become possible to study materials under highly nonequilibrium conditions. By suddenly introducing a known amount of energy into the system, the equilibrium state is disturbed and the subsequent relax- ation processes are then observed on timescales of structural and electronic responses. These experiments can deliver valuable information about the complex interactions between the different constituents of condensed matter, which would be inaccessible under equilibrium conditions. We use time resolved electron diffraction to investigate the behaviour of a CDW system perturbed by a short laser pulse. From the observed changes in the diffraction patterns we can directly deduce changes in the lattice structure of our sample. A femtosecond electron diffraction setup was developed at the Laser Research In- stitute in Stellenbosch, South Africa. Short laser pulses produce photo electrons which are accelerated to an energy of 30 keV. Despite space charge broadening effects, elec- tron pulses shorter than 500 fs at sample position can be achieved. Technical details of this system and its characterisation as well as sample preparation techniques and analysis methods are described in detail in this work. Measurements on two members of the quasi-two-dimensional transition metal di- chalcogenides, namely 4Hb-TaSe2 and 1T-TaS2, are shown and discussed. Both show fast (subpicosecond) changes due to the suppression of the PLD and a rapid heating of the lattice. When the induced temperature rise heats the sample above a phase tran- sition temperature, a complete transformation into the new phase was observed. For 4Hb-TaSe2 we found that the recovery to the original state is significantly slower if the PLD was completely suppressed compared to only disturbing it. On 1T-TaS2 we could not only study the suppression of the original phase but also the formation of the higher energetic CDW phase. Long (100 ps) time constants were found for the tran- sition between the two phases. These suggest the presence of an energy barrier which has to be overcome in order to change the CDW phase. Pinning of the CDW by de- fects in the crystal structure result in such an energy barrier and consequently lead to a phase of domain growth which is considerably slower than pure electron or lattice dynamics. / AFRIKAANSE OPSOMMING: Dit is bekend dat lae-dimensionele materie fase oorgange ondergaan na anders ge- ori¨enteerde toestande wanneer afgekoel word tot laer temperature. Hierdie fases toon dikwels ’n periodiese modulasie van die elektron digtheid (genoem ’n “charge density wave” – CDW), tesame met ’n periodiese effek op die kristalrooster (genoem ’n “peri- odic lattice distortion” – PLD). Alhoewel baie eksperimente al uitgevoer is en al baie geleer is oor hierdie CDW fase, is die redes vir hul bestaan nog steeds nie ten volle verstaan nie. Baie prosesse, wat of sterk elektron–elektron of elektron–fonon interaksie toon, is al waargeneem en kan ’n rol speel in die verduideliking van die vorming van die verskillende fases onder verskillende omstandighede. Met die beskikbaarheid van femtosekonde lasers is dit nou moontlik om materie onder hoogs nie-ewewig voorwaardes te bestudeer. Deur skielik ’n bekende hoeveel- heid energie in die stelsel in te voer, word die ewewigstaat versteur en word die daar- opvolgende ontspanning prosesse waargeneem op die tydskaal van atomies struktu- rele en elektroniese bewiging. Hierdie eksperimente kan waardevolle inligting lewer oor die komplekse interaksies tussen die verskillende atomiese komponente van ge- kondenseerde materie, wat ontoeganklik sou wees onder ewewig voorwaardes. Ons gebruik elektrondiffraksie met tyd resolusie van onder ’n pikosekonde om die gedrag van ’n CDW stelsel te ondersoek nadat dit versteur is deur ’n kort laser puls. Van die waargenome veranderinge in die diffraksie patrone kan ons direk aflei watse veranderinge die kristalstruktuur van ons monster ondergaan. ’n Femtosekonde elektronendiffraksie opstelling is ontwikkel by die Lasernavors- ingsinstituut in Stellenbosch, Suid-Afrika. Kort laser pulse produseer foto-elektrone wat dan na ’n energie van 30 keV versnel word. Ten spyte van Coulomb afstoting ef- fekte, kan elektron pulse korter as 500 fs by die monster posisie bereik word. Tegniese besonderhede van hierdie opstelling, tegnieke van die voorbereiding van monsters asook analise metodes word volledig in hierdie tesis beskryf. Metings op twee voorbeelde van kwasi-tweedimensionele semi-metale, naamlik 4Hb-TaSe2 en 1T-TaS2, word gewys en bespreek. Beide wys ’n vinnige (subpikosekon- de) verandering as gevolg van die versteuring van die PLD en ’n vinnige verhitting van die kristalrooster. Wanneer die ge¨ınduseerde temperatuur bo die fase oorgang tempe- ratuur styg, is ’n volledige transformasie na die nuwe fase waargeneem. Vir 4Hb-TaSe2 het ons gevind dat die herstelling na die oorspronklike toestand aansienlik stadiger is as die PLD heeltemal viernietig is in vergelyking met as die PLD net versteur is. Met 1T-TaS2 kon ons nie net alleenlik die vernietiging van die oorspronklike fase sien nie, maar ook die vorming van ’n ho¨er energie CDW fase. Lang (100 ps) tydkonstante is gevind vir die oorgang tussen die twee fases. Hierdie dui op die teenwoordigheid van ’n energie-versperring wat eers oorkom moet word om die CDW fase voledig te ver- ander. Vaspenning van die CDW deur defekte in die kristalstruktuur veroorsaak so’n energie versperring en gevolglik lei dit tot ’n fase van groeiende CDW gebiede wat heelwat stadiger as pure elektron of kritalrooster dinamika is.

<p>In this work, we study two important themes in the physics of the interacting one-dimensional (1D) electron gas: the transition from one-dimensional to higher dimensional behavior, and the role of inhomogeneity. The interplay between interactions, reduced dimensionality, and inhomogeneity drives a rich variety of phenomena in mesoscopic physics. In 1D, interactions fundamentally alter the nature of the electron gas, and the homogeneous 1D electron gas is described by Luttinger Liquid theory. We use Quantum Monte Carlo methods to study two situations that are beyond Luttinger Liquid theory --- the quantum phase transition from a linear 1D electron system to a quasi-1D zigzag arrangement, and electron localization in quantum point contacts. </p><p>Since the interacting electron gas has fundamentally different behavior in one dimension than in higher dimensions, the transition from 1D to higher dimensional behavior is of both practical and theoretical interest. We study the first stage in such a transition; the quantum phase transition from a 1D linear arrangement of electrons in a quantum wire to a quasi-1D zigzag configuration, and then to a liquid-like phase at higher densities. As the density increases from its lowest values, first, the electrons form a linear Wigner crystal; then, the symmetry about the axis of the wire is broken as the electrons order in a quasi-1D zigzag phase; and, finally, the electrons form a disordered liquid-like phase. We show that the linear to zigzag phase transition occurs even in narrow wires with strong quantum fluctuations, and that it has characteristics which are qualitatively different from the classical transition.</p><p>Experiments in quantum point contacts (QPC's) show an unexplained feature in the conductance known as the ``0.7 Effect''. The presence of the 0.7 effect is an indication of the rich physics present in inhomogeneous systems, and we study electron localization in quantum point contacts to evaluate several different proposed mechanisms for the 0.7 effect. We show that electrons form a Wigner crystal in a 1D constriction; for sharp constriction potentials the localized electrons are separated from the leads by a gap in the density, while for smoother potentials, the Wigner crystal is smoothly connected to the leads. Isolated bound states can also form in smooth constrictions if they are sufficiently long. We thus show that localization can occur in QPC's for a variety of potential shapes and at a variety of electron densities. These results are consistent with the idea that the 0.7 effect and bound states observed in quantum point contacts are two distinct phenomena.</p> / Dissertation

When cutting an ice from lakes and ponds gaseous phase displays often ubiquitous bubble textures along the ice thickness. The occurrence of bubbles (enclosures filled with the gas) in ice relates to a content of the dissolved gas in the lake/pond water prior to freezing over the surface. When water freezes, dissolved gases are rejected and redistributed at the ice-water interface, depending on the saturation ratio between the gas and water. If the concentration of dissolved gases surpasses a critical value (as freezing progresses), the water at the interface becomes supersaturated, and gas bubbles nucleate and grow to a visible size along the interface. The bubbles generated at the ice-water interface are either incorporated into the ice crystal as the ice-water interface advances, thus forming gas pores in the ice, or released from the interface. If there is incorporation or release is determined by several factors. The bubbles nucleated at the advancing ice-water interface may be characterized by concentration, shape, and size, which depend on growth rate of ice, the amount of gases dissolved in water, and the particulate content of water. This work focused on the relation between growth rates of the ice and the occurrence of bubbles in the pond ice. I monitored the temperature of the ice formed...

Syftet med denna undersökning är att undersöka hur undervisningen om partikelmodellen bedrivs i årskurserna 4–6 och hur undervisningen utformas. Studien genomfördes med hjälp av kvalitativt inriktade intervjuer med fem olika lärare som undervisar inom No-ämnena i de aktuella årskurserna. Resultatet visar att alla fem lärarna undervisar om fasövergångar och materians byggstenar, men att lärarna fördjupar sig inom olika delar av dessa områden.  Lärarna i undersökningen väljer olika undervisningsmetoder när de undervisar om partikelmodellen: Traditionell undervisning, hypoteser, datoranimeringar, laborationer, dramatiseringar och användning av konkret material. / The purpose with this paper has been to examine how the education about the particle model in grades 4–6 is conducted and how the education is carried out. The study was carried out with the help of qualitatively directed interviews with five teachers that teach in the science subjects in the grades in question. The results show that all five teachers teach about, phase transitions and the building blocks of matter, but choose to immerse in different parts of these subjects. The teachers choose different teaching methods to teach about the particle model: Traditional teaching, hypotheses, computer animations, laboratory, dramatization and use of concrete materials.

Misturas liotrópicas de laurato de potássio (KL)/ sulfato de potássio (K2SO4)/ álcool (CnH2n+1OH)/ água (H2O) apresentam fases no estado líquido cristalino nemático. Essas fases nemáticas foram colesterizadas através da adicão do agente quiral brucina à mistura. Este estudo foi realizado mantendo as frações molares de todos os constituintes das misturas constantes e variando o comprimento da mol´ecula de álcool entre oito (1-octanol) e dezesseis (1-hexadecanol) átomos de carbono. Três fases colestéricas foram identificadas: ChD (colestérica discótica), ChB (colestérica biaxial) e ChC (colestérica calamítica). O diagrama de fases foi construído em função do número de átomos de carbono n na molécula do álcool. As transições entre as fases colestéricas foram investigadas por medições das birrenfringências ópticas usando microscopia óptica de luz polarizada. As misturas com 9 n 12 apresentaram as três fases colestéricas como função da temperatura e uma região de crossover entre as fases ChD e ChB, com comprimento de correlação a temperatura nula maior do que as dimensões micelares típicas. Misturas com n=8 e n=13 apresentaram transição de fase de primeira ordem entre as fases ChD e ChC, sem a presença da fase ChB intermediária a elas. As misturas com n=14, 15 e 16 apresentaram somente a fase ChC como função da temperatura. Os resultados foram interpretados como consequência da nanosegregação das moléculas de álcool nas micelas com relação às moléculas do anfifílico principal. / Lyotropic mixtures of potassium laurate (KL)/ potassium sulphate (K2SO4)/ alcohol (CnH2n+1OH)/ water (H2O) present nematic liquid crystal phases. These nematic phases were cholesterized by the doping of the mixtures with the chiral agent brucine. This study was conducted by keeping constant the molar fractions of all constituents of the mixtures and varying the length of the alcohol molecule between eight (1-octanol) and sixteen (1-hexadecanol) carbon atoms. Three cholesteric phases were identified: ChD (discotic cholesteric), ChB (biaxial cholesteric), and ChC (calamitic cholesteric). The phase diagram was constructed as a function of the number of carbon atoms n in the alcohol molecule. The cholesteric-cholesteric phase transitions were investigated by measurements of the optical birefringences via polarized light microscopy. The mixtures with 9 n 12 presented the three cholesteric phases as a function of temperature and a crossover between the ChD and ChB phases, with a bare correlation length larger than the typical micellar dimensions. Mixtures with n =8 and n =13 exhibited first order phase transitions among the ChD and the ChC phases, without the presence of the intermediate ChB phase. Mixtures with n =14, 15 and 16 showed only the ChC phase as a function of temperature. These results were interpreted as a consequence of the nanosegregation of the alcohol molecules in the micelles with respect to the main amphiphilic molecules.

Este trabalho visou o estudo da resposta óptica não-linear de cristais líquidos liotrópicos nas fases isotrópicas e nemática calamítica e nas vizinhanças das transições de fase nemática calamítica isotrópica e nemática calamítica nemática biaxial. Para este estudo foi utilizada, fundamentalmente, a técnica de varredura Z. Os resultados obtidos indicam que o efeito não-linear em cristais líquidos liotrópicos esta ligado à presença de micelas na mistura e que a anisometria de micela tem influencia na resposta observada. Foi observado ainda que a presença de ferrofluido na mistura, mesmo em pequenas quantidades, causa um grande aumento na absorção óptica da amostra e consequentemente da resposta não-linear. O comportamento do índice de refração não-linear (n IND.2) em função da temperatura nas vizinhanças da transição da fase nemática calamítica para nemática biaxial apresenta um crescimento expressivo de (n IND.2). Nas vizinhanças da transição nemática calamítica para isotrópica esse efeito não foi observado. / This work has been focused on the study of the optical nonlinear response of lyotropic liquid crystals in the isotropic and nematic calamitic phases and in the neighborhood of the nematic calamitic isotropic and nematic calamitic nematic biaxial phase transitions. The basic technique we used is Z-scan. The results obtained indicated that the nonlinear effect in lyotropic liquid crystals is related to the presence of micelles in the mixture and the micelle anisotropy has influence on the observed response. Is has also been observed that the presence of ferrofluid in the mixture, even in small quantities, causes a large raise in the sample optical absorption and consequently in the nonlinear response. The behavior of the nonlinear refractive index (n IND.2) as function of temperature in the neighborhood of the nematic calamitic to nematic biaxial phase transition shows as expressive n IND.2 raise. This behavior has not been observed in the neighborhood of the nematic calamitic to isotropic phase transition.

Neste trabalho estudamos a influência do tamanho molecular médio sobre a natureza da transição de fase esmética A (SA)-colestérica (C) líquido-cristalina para os compostos termotrópicos de miristato de colesterila (C14), nonanoato de colesterila (C9) e misturas binárias de C14 e C9 e caproato de colesterila (C6) e C9. Medidas de microscopia óptica foram realizadas para determinar as temperaturas de transição de fase SA C e C-isotrópica (I). Isto possibilitou a escolha dos intervalos de temperatura próximos às transições de fases, como referências para as outras técnicas utilizadas no trabalho. A natureza das transições de fase (descontínua, também denominada de primeira ordem, ou contínua) foi inferida através das análises de medidas de densidade e entálpicas. Os resultados evidenciaram que a transição passa de primeira ordem para contínua quando o tamanho molecular médio e a temperatura reduzida, r (definida como a razão entre as temperaturas de transição de fases SA C e C I ), decrescem no sistema. A ocorrência de uma transição de fase SA C contínua foi observada para a concentração de 65% de C9 na mistura C6 C9, para o valor de r ~ 0, 92. Propriedades mesoscópicas dos compostos estudados, como a distância entre as camadas esméticas na fase SA, dSA, o tamanho molecular médio, , no domínio C, e o comportamento do tamanho de correlação, , ao longo das transições de fase, foram determinadas da análise dos picos de difração de raios X. Os dados revelaram que dSA diminui com o decréscimo do tamanho molecular médio, como era esperado. Além disso, os valores de obtidos na fase C, próximos à transição I C, concordam com os tamanhos moleculares médios calculados supondo que as moléculas estejam em conformação estendida. Mais ainda, foi observado um aumento no tamanho de correlação na fase C quando a temperatura é reduzida da fase I para a fase SA, representando um aumento no grau de ordem orientacional. Contudo, o parâmetro troca abruptamente na transição C SA. Tal descontinuidade diminui com o decréscimo do tamanho molecular médio (e assim com r). Para o sistema particular composto por 65% C9 : 35% C6, onde identificamos um transição de fase contínua SA C, observamos um comportamento de (T TSAC)0,5 no domínio da fase C, em bom acordo com a teoria de campo médio. / The influence of the mean molecular length on the nature of the smectic A (SA)- cholesteric (C) liquid crystal phase transition has been studied for cholesteryl myristate (C14), cholesteryl nonanoate (C9) and binary mixtures of C14 and C9 and cholesteryl caproate (C6) and C9. Optical microscopy was carried out to determine the temperatures of the SAC as weel as the C - isotropic (I) phase transitions. This allowed the choice of the optimum temperature interval near the phase transitions. Information concerning the nature of the transitions (descontinuous, also referred to as first order, or continuous) was evaluated through the analysis of the density and enthalpic measurements. The results have evidenced that the transition crosses over from first order to continuous when both the mean molecular length and the reduced temperature, r (ratio between SAC and CI phase transition temperatures), decrease in the system. The occurrence of a continuous SA C phase transition is observed for a concentration very near 63.1 molar percent of C9 in the C6 C9 mixture (65 wt% C9 : 35 wt% C6), at r ~ 0.92. Mesoscopic properties of the systems, as the distance between the smectic layers in the SA phase, dSA, the mean molecular length, , in the C domain, and the correlation length, , behavior along the phase transitons, were determined from the X-ray difraction peaks. The data have revealed that dSA decreases as the mean molecular length is reduced, as it was expected. Moreover, values obtained in the C phase near the I C phase transition agree with the mean molecular lengths calculated from the corresponding extended molecule lengths. In addition, an increase in the correlation length in the C phase is observed, as the temperature is reduced from I to SA phases, representing an increase in the orientational order. Nevertheless, the parameter jumps in the C SA phase transition. Such discontinuity decreases as the mean molecular length (and hence the reduced temperature) diminishes. For the particular system composed of 65 wt% C9 : 35 wt% C6, where a continuous SA C phase transition was identified, a behavior of (T TSAC)0,5 in the C domain was observed, in good agreement with the mean field theory.

Estudamos o modelo predador-presa estocástico definido em uma rede com interações entre os primeiros vizinhos, cada sítio podendo assumir três estados: vazio, ocupado por presa e ocupado por predador. Introduzimos ainda um parâmetro que controla a possibilidade de difuãao dos estados, a difusão é permitida entre quaisquer estados. O modelo exibe uma fase oscilante, uma fase não-oscilante e uma fase absorvente. As duas primeiras fases possibilitam a coexistência entre as espécies biológicas enquanto na fase absorvente a rede é totalmente preenchida por presas e o sistema fica preso nessa configuração. Determinamos a linha de transição da fase não-oscilante para a fase absorvente por meio de simulações dependentes do tempo. Também, determinamos a linha de transição da fase oscilante para a fase não-oscilante através da análise das funções de autocorrelação das séries temporais de presas e predadores. Além disso, estudamos o modelo por meio de aproximações de campo médio dinâmico. Concluímos que a inclusão da difusão no modelo predador-presa leva a uma maior região de coexistência das espécies no diagrama de fases. Nossos resultados sugerem que o componente difusivo é irrevelevante quanto ao comportamento crítico, pois ele não exclui o modelo da classe de universalidade da percolação direcionada. / We have studied the predator-prey stochastic model defined on a lattice with first neighbour interactions. Each site of the lattice may assume one of three states: vacant, occupied by prey and occupied by predator. We have introduced a parameter that controls the possibility of difusion among sites. The model shows an oscilating phase, a non-oscilating phase and an absorbing phase. In the first two phases the system exhibits coexistence of biological species while in the absorbing phase the lattice is filled with prey and the system becomes trapped. We have determined the transition line between the non-oscilating and absorbing phases using time-dependent simulations. We have also determined the transition lines between oscilating and non-oscilating phases using time-autocorrelation functions of the prey time-series. In addition, we have studied the model by means of dynamical mean-field aproximations. We conclude that the introduction of diffusion in the predator-prey model leads to a larger region of coexistence in the phase diagram. Our results suggest that difusion is irrelevant for the critical behavior since it does not change the universatility class of the model.