No description available.

Spin glasses have been the subject of intense study and considerable controversy for decades, and the low-temperature phase of short-range spin glasses is still poorly understood. Our main goal is to improve our understanding in this area and find an answer to the following question: Are there only a single pair or a countable infinity of pure states in the low temperature phase of the EA spin glass? To that aim we first start by introducing spin glasses and provide a brief history of their research, then proceed to describe our method of simulation, the parallel tempering Monte Carlo algorithm. Next, we present the results of a large-scale numerical study of the equilibrium three-dimensional Edwards-Anderson Ising spin glass with Gaussian disorder. In order to understand how the parallel tempering algorithm works, we measure various static, as well as dynamical quantities, such as the autocorrelation times and round-trip times for the parallel tempering Monte Carlo method. We examine the correlation between static and dynamic observables for _ 5000 disorder realizations and up to 1000 spins down to temperatures at 20% of the critical temperature, and our results show that autocorrelation times are directly correlated with the roughness of the free-energy landscape. In the following chapters, the three- and four-dimensional Edwards-Anderson and mean-field Sherrington-Kirkpatrick Ising spin glasses are studied again via large-scale Monte Carlo simulations at low temperatures, deep within the spinglass phase. Performing a careful statistical analysis of several thousand independent disorder realizations and using an observable that detects peaks in the overlap distribution, we show that the Sherrington-Kirkpatrick and Edwards-Anderson models have a distinctly different low-temperature behavior. We arrive to the following conclusion: The structure of the spin-glass overlap distribution for the Edwards-Anderson model suggests that its low-temperature phase has only a single pair of pure states. Finally we present results for several new observables, along with a few preliminary studies and suggestions for future research.

Nesta tese utilizamos o modelo do replicador aleatório, proposto por Diederich e Opper, para analisar as propriedades de equilíbrio de ecossistemas complexos (formados por um grande número de espécies) em três situações distintas. Na primeira parte desta tese, investigamos os efeitos de interações variáveis sobre a estrutura do ecossistema, utilizando o método de réplicas generalizado, introduzido por Penney et al. Este formalismo propõe uma nova interpretação para o índice de réplicas n, a saber, como sendo a razão entre duas temperaturas características: a temperatura relacionada aos acoplamento e a temperatura associada às variáveis de spin. Empregando t\\\'ecnicas de campo m\\\'edio de Mec\\^anica Estat\\\'stica e tamb\\\'em simula\\c\\~oes num\\\'ericas tratamos, em particular, do estado fundamental ($\\beta ightarrow + \\infty$). Encontramos dois regimes distintos, um onde prevalece a coopera\\c\\~ao entre as diferentes esp\\\'ecies ($\\beta^{\\prime} > 0$) e outro no qual a competi\\c\\~ao \\\'e predominante ($\\beta^ < 0$). No primeiro caso temos uma transi\\c\\~ao descont\\\'{\\i}nua para um regime de diversidade nula e no outro temos uma m\\\'axima diversidade das esp\\\'ecies. Na segunda parte desta tese \\cite, estudamos as implica\\c\\~oes de uma temperatura finita sobre a estrutura do ecossistema. Utilizamos a regra de Hebb para descrever as intera\\c\\~oes entre as diferentes esp\\\'ecies. A temperatura surge, no modelo, atrav\\\'es de um ru\\\'do gaussiano introduzido na equa\\c\\~ao estoc\\\'astica que rege a din\\^amica do processo. Tratamos analiticamente o caso recozido ({\\em annealed}), no qual as caracter\\\'sticas das esp\\\'ecies evoluem t\\~ao rapidamente quanto suas concentra\\c\\~oes, e o caso temperado ({\\em quenched}), onde tais caracter\\\'sticas est\\~ao fixas. Conclu\\\'{\\i}mos que h\\\'a uma transi\\c\\~ao de fase descont\\\'{\\i}nua entre um estado onde a competi\\c\\~ao prevalece, determinando baixa diversidade, para outro estado onde predomina a coopera\\c\\~ao. Por fim \\cite, analisamos as poss\\\'veis consequ\\^encias de uma interven\\c\\~ao humana sobre as propriedades de equil\\\'{\\i}brio do ecossistema. Admitimos o princ\\\'pio da exclus\\~ao competitiva para modelar os acoplamentos entre as diferentes esp\\\'ecies, a regra de Hebb. Interferimos na comunidade impondo que um conjunto de caracteres, selecionados previamente, esteja presente em uma fra\\c\\~ao bem definida dos seus membros. O principal resultado deste estudo revela, desde que o par\\^ametro de competi\\c\\~ao entre indiv\\\'duos semelhantes n\\~ao seja muito pequeno, que o efeito de uma tal manipula\\c\\~ao conduz a perda da diversidade e, portanto, ao empobrecimento do ecossistema. / In this thesis we use the random replicator model, proposed by Diederich and Opper \\cite, to analyse the equilibrium properties of complex ecosystems (formed by a large number of species) in three distinct situations. In the first part of this thesis \\cite, we investigate the effects of variable interactions upon ecosystem structure, using the generalized replica method, introduced by Penney et al \\cite. In this formalism we find a new interpretation for the replica number $n$ as the ratio between two characteristic temperatures: the temperature related to the couplings ($\\beta^$) and the temperature associated to the spin variables ($\\beta$). We approach the problem using mean field methods of statistical mechanics and intensive numerical simulations; in particular we are concerned with the ground state ($\\beta ightarrow + \\infty$). We find two distinct regimes, one where cooperation between different species prevails ($\\beta^ > 0$) and the other in which competition is predominant ($\\beta^ < 0$). In the first case we have a discontinuous transition to the zero diversity regime and in the other we have the maximum species diversity. In the second part of this thesis \\cite, we examine the finite temperature implications upon ecosystem structure. Through the Hebb rule we can describe the interactions between different species. With the aid of a Gaussian noise in the stochastic equation, that governs the temporal evolution, we have a way to introduce the finite temperature in the model. We treat analytically the annealed case, in which the species characteristics evolve so fast as its concentrations, as well as the quenched case, in which such characteristics are fixed. We conclude that there is a discontinuous phase transition between a state where competition prevails, implying low diversity, to another state in which cooperation is stronger. At last \\cite, we analyse the possible consequences of human intervention upon the equilibrium properties of the ecosystem. We assume the competitive exclusion principle to model the couplings between different species, the Hebb rule. We interfere in the community by imposing that a set of characters, previously selected, be present in a well defined fraction of its members. The main result of this study reveals, provided that the intraspecies competition parameter is not too weak, that the effect of such a manipulation leads to the impoverishment of the ecosystem.

Complex oxides represent an intersection of play grounds for the existence of exciting new fundamental physics and materials with potential technological implications. The realization of many exciting properties of these systems rely on the coupling of electronic, structural and magnetic degrees of freedom. Additionally, competing interactions within each type of coupling discussed previously lead to theoretically diverse ground states, which under the application of an external perturbation, can be tuned and probed. Ca3Co¬2-xMnxO6 represent a quasi-one dimensional Ising spin chain system oriented in an antiferromagnetic triangular lattice. The exotic behavior of the undoped compound Ca3Co2O6 has inspired work on continuing the fundamental understanding of frustrated magnetic systems. Through chemical doping of Manganese ions, the magnetic properties, namely the exotic spin glass like behavior can be enhanced for a modest doping range of x The effects of particle dimensionality were probed through the application of varied calcining conditions as to attempt to observe the altering of magnetic properties, mainly the out of equilibrium magnetization plateaus observed in Ca3Co1.75 Mn0.25O6. It appears that within the particle sizes studied the magnetic behavior is highly robust, even considering the inclusion of ionic disorder.

Nesta tese utilizamos o modelo do replicador aleatório, proposto por Diederich e Opper, para analisar as propriedades de equilíbrio de ecossistemas complexos (formados por um grande número de espécies) em três situações distintas. Na primeira parte desta tese, investigamos os efeitos de interações variáveis sobre a estrutura do ecossistema, utilizando o método de réplicas generalizado, introduzido por Penney et al. Este formalismo propõe uma nova interpretação para o índice de réplicas n, a saber, como sendo a razão entre duas temperaturas características: a temperatura relacionada aos acoplamento e a temperatura associada às variáveis de spin. Empregando t\\\'ecnicas de campo m\\\'edio de Mec\\^anica Estat\\\'stica e tamb\\\'em simula\\c\\~oes num\\\'ericas tratamos, em particular, do estado fundamental ($\\beta ightarrow + \\infty$). Encontramos dois regimes distintos, um onde prevalece a coopera\\c\\~ao entre as diferentes esp\\\'ecies ($\\beta^{\\prime} > 0$) e outro no qual a competi\\c\\~ao \\\'e predominante ($\\beta^ < 0$). No primeiro caso temos uma transi\\c\\~ao descont\\\'{\\i}nua para um regime de diversidade nula e no outro temos uma m\\\'axima diversidade das esp\\\'ecies. Na segunda parte desta tese \\cite, estudamos as implica\\c\\~oes de uma temperatura finita sobre a estrutura do ecossistema. Utilizamos a regra de Hebb para descrever as intera\\c\\~oes entre as diferentes esp\\\'ecies. A temperatura surge, no modelo, atrav\\\'es de um ru\\\'do gaussiano introduzido na equa\\c\\~ao estoc\\\'astica que rege a din\\^amica do processo. Tratamos analiticamente o caso recozido ({\\em annealed}), no qual as caracter\\\'sticas das esp\\\'ecies evoluem t\\~ao rapidamente quanto suas concentra\\c\\~oes, e o caso temperado ({\\em quenched}), onde tais caracter\\\'sticas est\\~ao fixas. Conclu\\\'{\\i}mos que h\\\'a uma transi\\c\\~ao de fase descont\\\'{\\i}nua entre um estado onde a competi\\c\\~ao prevalece, determinando baixa diversidade, para outro estado onde predomina a coopera\\c\\~ao. Por fim \\cite, analisamos as poss\\\'veis consequ\\^encias de uma interven\\c\\~ao humana sobre as propriedades de equil\\\'{\\i}brio do ecossistema. Admitimos o princ\\\'pio da exclus\\~ao competitiva para modelar os acoplamentos entre as diferentes esp\\\'ecies, a regra de Hebb. Interferimos na comunidade impondo que um conjunto de caracteres, selecionados previamente, esteja presente em uma fra\\c\\~ao bem definida dos seus membros. O principal resultado deste estudo revela, desde que o par\\^ametro de competi\\c\\~ao entre indiv\\\'duos semelhantes n\\~ao seja muito pequeno, que o efeito de uma tal manipula\\c\\~ao conduz a perda da diversidade e, portanto, ao empobrecimento do ecossistema. / In this thesis we use the random replicator model, proposed by Diederich and Opper \\cite, to analyse the equilibrium properties of complex ecosystems (formed by a large number of species) in three distinct situations. In the first part of this thesis \\cite, we investigate the effects of variable interactions upon ecosystem structure, using the generalized replica method, introduced by Penney et al \\cite. In this formalism we find a new interpretation for the replica number $n$ as the ratio between two characteristic temperatures: the temperature related to the couplings ($\\beta^$) and the temperature associated to the spin variables ($\\beta$). We approach the problem using mean field methods of statistical mechanics and intensive numerical simulations; in particular we are concerned with the ground state ($\\beta ightarrow + \\infty$). We find two distinct regimes, one where cooperation between different species prevails ($\\beta^ > 0$) and the other in which competition is predominant ($\\beta^ < 0$). In the first case we have a discontinuous transition to the zero diversity regime and in the other we have the maximum species diversity. In the second part of this thesis \\cite, we examine the finite temperature implications upon ecosystem structure. Through the Hebb rule we can describe the interactions between different species. With the aid of a Gaussian noise in the stochastic equation, that governs the temporal evolution, we have a way to introduce the finite temperature in the model. We treat analytically the annealed case, in which the species characteristics evolve so fast as its concentrations, as well as the quenched case, in which such characteristics are fixed. We conclude that there is a discontinuous phase transition between a state where competition prevails, implying low diversity, to another state in which cooperation is stronger. At last \\cite, we analyse the possible consequences of human intervention upon the equilibrium properties of the ecosystem. We assume the competitive exclusion principle to model the couplings between different species, the Hebb rule. We interfere in the community by imposing that a set of characters, previously selected, be present in a well defined fraction of its members. The main result of this study reveals, provided that the intraspecies competition parameter is not too weak, that the effect of such a manipulation leads to the impoverishment of the ecosystem.

No description available.

Phase transitions and their associated critical phenomena are of fundamental importance and play a crucial role in the development of statistical physics for both classical and quantum systems. Phase transitions embody diverse aspects of physics and also have numerous applications outside physics, e.g., in chemistry, biology, and combinatorial optimization problems in computer science. Many problems can be reduced to a system consisting of a large number of interacting agents, which under some circumstances (e.g., changes of external parameters) exhibit collective behavior; this type of scenario also underlies phase transitions. The theoretical understanding of equilibrium phase transitions was put on a solid footing with the establishment of the renormalization group. In contrast, non-equilibrium phase transition are relatively less understood and currently a very active research topic. One important milestone here is the Kibble-Zurek (KZ) mechanism, which provides a useful framework for describing a system with a transition point approached through a non-equilibrium quench process. I developed two efficient Monte Carlo techniques for studying phase transitions, one is for classical phase transition and the other is for quantum phase transitions, both are under the framework of KZ scaling. For classical phase transition, I develop a non-equilibrium quench (NEQ) simulation that can completely avoid the critical slowing down problem. For quantum phase transitions, I develop a new algorithm, named quasi-adiabatic quantum Monte Carlo (QAQMC) algorithm for studying quantum quenches. I demonstrate the utility of QAQMC quantum Ising model and obtain high-precision results at the transition point, in particular showing generalized dynamic scaling in the quantum system. To further extend the methods, I study more complex systems such as spin-glasses and random graphs. The techniques allow us to investigate the problems efficiently. From the classical perspective, using the NEQ approach I verify the universality class of the 3D Ising spin-glasses. I also investigate the random 3-regular graphs in terms of both classical and quantum phase transitions. I demonstrate that under this simulation scheme, one can extract information associated with the classical and quantum spin-glass transitions without any knowledge prior to the simulation.

Neste trabalho utilizam-se duas adaptações do modelo originalmente proposto por van Hemmen com o intuito de investigar os efeitos de um campo aleatório hi sob as transições de fases: um modelo com spin 1 estudado na versão clássica e um modelo na formulação fermiônica. A escolha do modelo de van Hemmen está relacionada ao fato de que não e necessário utilizar o método das réplicas para tratar a desordem. No primeiro caso, o modelo clássico conta com um campo cristalino (D) que favorece energeticamente os estados não interagentes. As interações aleatórias Ji j são respons aveis por introduzir desordem e frustração ao problema. Tanto as variáveis aleatórias quanto o campo aleatório seguem uma distribuição de probabilidades bimodal. Analisando o comportamento dos parâmetros de ordem e da energia livre, diagramas de fases da temperatura pelo acoplamento ferromagnético J0 e pelo campo cristalino D para diferentes valores de hi foram construídos. Os resultados indicam que a presença do campo aleatório tende a reduzir o ponto tricrítico das transições de fases e, para determinado valor de hi, uma nova solução da fase vidro de spin (VS) pode ser favorecida. Além disso, para valores relativamente altos de hi, o problema apresenta pontos multicríticos nas transições de fase. Também busca-se investigar nesse modelo se o mesmo e capaz de apresentar algum tipo de transição inversa (TI) As TI são uma classe de transições de fases altamente contraintuitivas, em que uma fase usualmente ordenada tem entropia maior que uma fase desordenada. Elas se manifestam nos diagramas de fases através de uma reentrância da fase desordenada-ordenada-desordenada conforme a temperatura diminui. Embora o modelo apresente diversos pontos tricríticos na transição PM/VS, nenhum tipo de transição reentrante foi observada, não havendo, portanto, nenhuma evidência de transição inversa no sistema. Já o modelo analisado na formulação fermiônica conta com um potencial químico (m), que controla a diluição magnética relacionada ao favorecimento dos sítios duplamente ocupados ou vazios, e com um campo magnético transverso G, que introduz flutuações quânticas ao problema. Nesse caso, as interações de spin Ji j e o campo aleatório seguem uma distribuição gaussiana. A introdução do campo hi, a nível de campo médio, permite investigar as TI sob os efeitos de uma desordem que não e uma fonte de frustração Os resultados mostram uma transição reentrante da fase VS para a fase paramagnética (PM) na ausência de G e hi. A reentrância aparece para um certo intervalo de m, em que se encontra uma fase PM a baixas temperaturas com menor entropia do que a fase VS, caracterizando a transição do tipo congelamento inverso (CI). No entanto o CI e gradualmente suprimido quando os efeitos hi são intensificados. Além disso, o CI e completamente destruído pelas flutuações quânticas provenientes do G. Dessa forma, a desordem combinada com a diluição pode apresentar um cenário favorável a ocorrência de CI, enquanto o campo aleatório e as flutuações quânticas agem contra este tipo de transição. / In this work, two adaptations to the original model proposed by van Hemmen are used with the aim of investigating the e ects of a random eld hi under the phase transitions: a model studied in the classical version and a model in the fermionic formulation. The van Hemmen model was chosen because the disorder can be treated without the use of the replica method. In the rst case, the classic model has a crystal eld (D) which energetically favors the non-interacting states. The random interactions Ji j are responsible for introduce disorder and frustration to the problem. Both random eld and random variables follow a bimodal probability distribution. Analyzing the behavior of the order parameters and the free energy, phase diagrams of temperatura T versus the ferromagnetic coupling J0 and T versus the crystal eld D for di erent values of hi were build. The results indicate that the presence of the random eld tends to reduce the tricritical point of the phase transitions. For a given value of hi, a new solution of phase spin glass (SG) can be favored. In addition, for su ciently high enough values of hi the problem presents multicritical points in phase transitions. It is also intended to investigate if this model is able to present some kind of inverse transition (IT) IT is a class of highly nonintuitive phase transitions in that the usual ordered phase has more entropy than the disordered one. The IT manifests in the phase diagrams as a reentrance of the disordered-ordereddisordered phase according to the temperature decreases. Although the model presents several tricritical points in the transition PM=SG, no type of reentrant transition was observed. Therefore, there is no evidence of inverse transition in this model. The model analyzed in the fermionic formulation has a chemical potential (m), which has the role of controlling the magnetic dilution related to favoring double-occupation or empty sites. This model also counts with a transverse magnetic eld G, which introduces quantum uctuations to the problem. In this case, the spin interactions Ji j and random eld follow a Gaussian distribution The introduction of the hi allows the investigation of IT under the e ects of a disorder that is not a source of frustration. The results show a reentrant transition from the SG phase to the PM phase in the absence of G and hi. The reentrance appears for a certain range of m, in which there is a PM phase at low temperatures with lower entropy than the SG phase, characterizing the inverse freezing (IF) transition. However, IF is gradually suppressed when the e ects hi are intensi ed. Moreover, the IF is completely destroyed by quantum uctuations from G. Thus, the disorder combined with the dilution may present the favorable scenario to the occurrence of IF, while the random eld and the uctuations quantum mechanics act against this kind of transition.

不同於一般電腦的數位位元資訊只有兩種可能數值0與1，量子電腦利用的是量子位元，係一個二維希爾伯特(Hilbert)空間中的單位向量，其表示方法為0與1的線性疊加態。量子模擬利用量子物理的基本線性疊加原理，來得到更有效率的方法處理計算科學的問題。本論文討論兩種量子演算法，量子隨機行走法則與量子退火最佳化演算法，在本論文中分成兩大部分，在第一部分中，我們研究在各種圖像中的量子隨機行走法則。研究隨機漫步有助於我們了解各種自然界中的隨機過程，如擴散作用與布朗運動。隨機漫步也已經被運用在許多的電腦演算法中，如搜尋演算法或者最佳化演算法。量子的隨機漫步係建立於量子力學的波函數，也是古典隨機漫步原理的延伸。但古典與量子隨機漫步卻有著非常不同的特性，比如量子隨機漫步傳播的速度大於古典的隨機漫步，且量子隨機漫步並不會像古典隨機漫步一樣會趨向穩定態。量子隨機漫步的時間演進係一由么正(unitary)算符所規範的么正過程，根據定義的不同，我們區分離散時間與連續時間兩種量子隨機漫步。在本論文中，我們研究與比較古典與量子的隨機漫步，分析在圖像以及無序環境上的模擬行走。第二部分，我們利用量子退火式演算解最佳化問題。退火係一材料從高溫控制降溫速度使其保持平衡態最後達成完美結晶結構的物理過程。與傳統的退火演算法利用熱擾動的方法不同，量子退火演算法利用的是量子擾動，使系統在其各種可能的解之間穿隧(tunneling)，以有效的達到最佳解。在本論文中，我們利用建立於路徑積分的蒙地卡羅(Monte Carlo)量子退火演算法，找出自旋玻璃的基態能量。我們以離散的虛數時間方法進行標準的量子蒙地卡羅以及連續的虛數時間方法進行路徑積分的蒙地卡羅，將這兩種量子方法與退火演算法結果的做分析比較。 / In standard classical digital computing, a unit of information takes only two possible values, say 0 or 1; In quantum computing, a unit of quantum information is a quantum bit or qubit, which is a unit vector in a two-dimensional Hilbert space, and is represented as a superposition of 0 and 1. Quantum simulation exploits the laws of quantum mechanics that involve the superposition principle to carry out computational tasks in a more efficient way than is possible with classical computers. This thesis is concerned with two quantum algorithms: quantum walks and quantum adiabatic optimization. This thesis is organized into two parts. In Part I, we study quantum walks on various graphs. Random walks are useful in understanding stochastic processes such as diffusion and Brownian motion. They have also been applied to many computational algorithms, such as search algorithms and algorithms for optimization problems. Quantum walks described by quantum mechanical wave functions are an extension of classical random walks. They have very different properties from classical random walks; for example, they do not in general converge toward a stationary distribution and potentially spread much faster. Quantum evolution is unitary; depending on the definition of unitary evolution operators, one distinguishes between discrete-time and continuous-time versions of quantum walks. We study these two versions of quantum walks. Quantum walks and classical random walks are compared in many examples, ranging from random walks on graphs to walks in disordered media. In Part II, we focus on optimization by quantum adiabatic algorithms (also known as quantum annealing algorithms). Annealing is a technique involving controlled cooling of a material to have perfect crystalline structures formed. Unlike classical simulated annealing in which thermal fluctuations are utilized for convergence in optimization problems, quantum annealing uses quantum fluctuations to explore the solution space via quantum tunneling, with the potential to hasten convergence to the best solution. In this thesis we implement quantum annealing based on path-integral quantum Monte Carlo (QMC) methods to find the ground states of Ising spin glasses. In particular, we investigate the effect of the discretization of imaginary time used in standard QMC methods and also perform continuous-time path integral Monte Carlo. We compare the results with those obtained by simulated annealing.

The system LiHo_<em>x</em>Y_1-<em>x</em>F₄ is a nearly perfect example of a dilute, dipolar-coupled Ising magnet and, as such, it is an ideal testing ground for many theories in statistical mechanics. At low holmium concentration (<em>x</em> = 0. 045) an unusual spin liquid or "anti-glass" state was discovered in previous work [1]. This state does not exhibit a spin glass freezing transition as is expected for a long-range interaction. Instead, it shows dynamics which are consistent with a collection of low-frequency oscillators [2]. It was also seen to have sharp features in its specific heat [3]. <br /><br /> We present heat capacity measurements on three samples at and around the concentration of the spin liquid state in zero magnetic field and in a temperature range from around 50 mK to 1 K. In contrast to previous measurements, we find no sharp features in the specific heat. The specific heat is a broad feature which is qualitatively consistent with that of a spin glass. The residual entropy as a function of <em>x</em>, obtained through a numerical integral of the data, however, is consistent with numerical simulations which predict a disappearance of spin glass ordering below a critical concentration of dipoles [4]. <br /><br /> Also presented here, is ac susceptibility data on an <em>x</em> = 0. 45 sample which exhibits a paramagnetic to ferromagnetic transition and is found to be consistent with previous work.