Thesis (M.S.)--University of Wisconsin--Madison, 1983. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 60-61).

Dissertação (mestrado)—Universidade de Brasília, Instituto de Física, Programa de Pós-Graduação em Física, 2014. / Submitted by Ana Cristina Barbosa da Silva (annabds@hotmail.com) on 2014-10-13T18:16:43Z No. of bitstreams: 1 2014_ManuelaCarvalhodeAlmeida.pdf: 659048 bytes, checksum: 34e03788488d8be7194500016ead00a9 (MD5) / Approved for entry into archive by Tania Milca Carvalho Malheiros(tania@bce.unb.br) on 2014-10-20T12:17:09Z (GMT) No. of bitstreams: 1 2014_ManuelaCarvalhodeAlmeida.pdf: 659048 bytes, checksum: 34e03788488d8be7194500016ead00a9 (MD5) / Made available in DSpace on 2014-10-20T12:17:09Z (GMT). No. of bitstreams: 1 2014_ManuelaCarvalhodeAlmeida.pdf: 659048 bytes, checksum: 34e03788488d8be7194500016ead00a9 (MD5) / Numa cadeia de spins XY fechada com um número N finito de sítios, condições de contorno desempenham um papel importante. Na literatura, os termos de fronteira são descartados. Além disto, existe uma correspondência entre teorias de gauge não-abeliana e cadeias de spin. O objetivo deste trabalho é prover um embasamento teórico sobre férmionse sistemas de spin para estudar esta correspondência no futuro e mostrarcomo teorias de gauge emergem de sistemas com número finitode graus de liberdade. Na cadeia de spin XY, focamos em discutir ostermos de fronteira, pois eles tem uma importância fundamental para o entendimento do modelo XY, explicando o aparecimento de degenerescências, além de mostrar que o limite termodinâmico pode esconder sutilezas. ______________________________________________________________________________ ABSTRACT / In a closed XY spin chain with finite number N of sites, boundary conditionsplay a crucial role. In the literature, these boundary term arediscarded. Furthermore, there is a correspondence between nonabeliangauge theories and spin chains. Therefore, there is a correspondencebetween non-abelian gauge theory and spin chains. Our goal in thiswork is to provide a theoretical basis on fermions and spin systems inonder to study this correspondence in the future. In addition, to showhow gauge theory can emerge from systems with a finite number ofdegrees of freedom. In spin chain XY, we focus on discussing the boundarytermos, since they are fundamental to the understanding of the XYmodel, because they explain the degeneracies of the model. In addition,the thermodynamic limit can hide subtleties.

ABSTRACT The phase transition of the antiferromagnetic-torsional XY model is studied with molecular dynamics. In the process of releasing energy, we find a minimally stable state. The minimally stable state indicates the process of disordered state to ordered state when the 2nd phase transition was derived. The temperature of phase transition for the iferromagnetic-torsional XY model is lower than that for the antiferromagnetic XY model. A increase of the coefficient J2 will delay the temperature of phase transition for the antiferromagnetic-torsional XY model .

Em decorrência do grande avanço alcançado pela mecânica estatística devido a introdução das idéias de invariância conforme às teorias de escala para sistemas finitos, retomamos, neste trabalho, o estudo do modelo XY em campo transverso. A princípio, apresentamos uma análise detalhada do comportamento \"crossover\" característico do modelo, onde incluímos cálculos melhorados dos expoentes da susceptibilidade e do gap de energia anteriormente apresentados por dos Santos e Stinch-combe. Em seguida, uma análise numérica do espectro foi desenvolvida, considerando-se condições livres de contorno, e comparada com as previsões da invariância conforme. Finalmente, as correções à energia do estado fundamental de cadeias finitas foram utilizadas para obter o parâmetro que caracteriza as classes de universalidade (a carga central c). / In view of the great advance attached from statistical mechanics due to the conformal invariance ideas introduced to the scale theories, we take over at this work, the study of the XY model in a transverse field. At first, we present a detailed analysis on the sample\'s typical crossover behavior. An improved calculation of the susceptibility and gap exponents early presented by dos Santos and Stinchcombe is included. Nest, a numerical analysis of the spectrum, regarding free boundary condi¬tions was developed and compared with conformal invariance predictions. Finally, the fundamental state energy corrections of finite chains were used to obtain the parameter which ,distingoishes the universality classes (the central charge c).

Cette thèse présente une étude du modèle XY bidimensionnel dans des conditions réalistes, comme la présence d'imperfections (impuretés non magnétiques) ou la taille finie du réseau. Ces deux aspects sont typiques de situations expérimentales et nécessitent un questionnement théorique. Nous avons également considéré le comportement a basse température du modèle d'Heisenberg fini et avons trouve un comportement analogue a celui du modèle XY. Nous avons utilise a la fois une approche analytique et des simulations numériques pour traiter le problème. Les résultats essentiels de ce travail sont: (a) la détermination de l'exposant de décroissance algébrique de la fonction de corrélation du modèle XY dilue, analytiquement avec l'approximation d'ondes de spins et par simulations Monte Carlo a l'aide de l'algorithme de Wolff, (b) l'estimation correspondante dans le cas du modèle d'Heisenberg sur réseau fini a basse température assortie de simulations numériques également, (c) la forme de l'interaction entre les impuretés non magnétiques et les défauts topologiques dans le cadre du modèle de Villain et dans le modèle de Kosterlitz-Thouless, et l'estimation analytique de la réduction de température critique basée sur la forme de cette interaction, (d) la détermination numérique de la distribution de probabilité de l'aimantation résiduelle sur un système fini en présence de désordre. Pour l'ensemble de nos travaux, nous avons obtenu un bon accord entre les prédictions théoriques et les simulations numériques, de même qu'avec des travaux antérieurs le cas écheant. / The thesis presents a study of the two-dimensional XY model exposed to such realistic conditions as the presence of lattice imperfections (nonmagnetic impurities) and lattice finiteness. Both features are typical for experimentally accessible magnetic materials and ask for theoretical description. We also have explored the low-temperature behaviour of a finite two-dimensional Heisenberg model and found behaviour similar to that of the 2D XY model. We have used both analytical and computer experiment approaches to tackle the problem. The essential output of the work consists of: (a) estimation of the non-universal exponent of the power law decay of the pair correlation function of a diluted 2D XY model at low temperature as a function of dilution, analytically in the spin-wave approximation, and in the Monte Carlo simulations using the Wolff algorithm; (b) analytical estimation of the corresponding exponent of the 2D Heisenberg model in the low-temperature limit for the finite lattice size and its comparison to the Monte Carlo simulations; (c) evaluation of the form of interaction between nonmagnetic impurities and topological defects within the Villain model as well as in the Kosterlitz-Thouless model, and analytical prediction of the critical temperature reduction made on the basis of this interaction; (d) Monte Carlo investigation of the form of the residual magnetization probability distribution in a finite system in presence of nonmagnetic disorder (dilution). We found all our analytical predictions in quite well agreement with the Monte Carlo simulation results as well as with other researches of the similar problems.

Les travaux exposés dans ce manuscrit sont consacrés à l'étude de la dynamique hors équilibre de chaînes quantiques décrites par le modèle XY. Nous commençons par considérer la dynamique unitaire obtenue par la mise en contact de sous-systèmes voisins thermalisés à des températures différentes. L'état initial de la chaîne est inhomogène et la dynamique tend à l'homogénéisation. Lorsque le système est initialement divisé en deux sous-systèmes semi-infini préparés aux températures T_b=\infty et T_s, nous obtenons analytiquement la fonction de Green associée à l'évolution du profil d'aimantation. Les résultats sont généralisés pour les températures T_b finies. Dans le cas particulier où T_s=T_b=0, nous étudions le comportement de l'entropie d'intrication entre sous-systèmes. Cette quantité présente un accroissement "rapide", prédit par la théorie conforme (dans le cas d'un système critique), suivi d'une relaxation algébrique vers la valeur d'équilibre. Dans la dernière partie la dynamique du système est obtenue par l'interaction avec l'environnement, décrite par le processus d'interactions répétées. Nous examinons la structure de la matrice densité du système et donnons une équation d'évolution de l'ensemble des corrélateurs à deux points. Finalement, nous étudions l'évolution temporelle du modèle XX en contact avec un ou deux bains aux températures T_1 et T_2. Lorsque T_1=T_2, l'étude du comportement du système, pour les temps courts, dévoile l'état stationnaire. Dans la situation T_1\ne T_2, nous vérifions numériquement que le profil d'aimantation est plat et proposons l'introduction d'un désordre dynamique qui permet l'installation d'un gradient d'aimantation. / The work exposed in this thesis is focused on the analyze of the non-equilibrium dynamics of quantum spin chains described by the XY model. We start by considering the unitary dynamics obtained by the interaction of neighboring sub-systems thermalized at different temperatures. The initial state is inhomogeneous and the dynamics is evolving towards an homogeneous state. For a system, initially divided in two sub-systems thermalized at the temperatures T_b=\inflty and T_s, we obtain the analytic expression of the Green function associated to the evolution of the magnetization profile. This results are generalized for finite temperatures T_b. In the particular case T_b=T_s=0, we analyze the behavior of the entenglement entropy generated between sub-systems. This quantity presents a fast increase, predicted by the conformal theory, followed by a slow relaxation towards equilibrium. In the last part, the dynamics of the system is obtained by the interaction with the environment, descibed by the process of repeated interactions. We are analyzing the structure of the system density matrix and are giving the equation of evolution for the set of two-points correlators. Finally, we study the time evolution of the XX model in contact with two baths at the temperatures T_1 and T_2. For T_1=T_2, the analysis of the short time behavior reveals useful informations on the stationary state. For T_1\ne T_2 we numericaly check that the density profil is flat and propose the introduction of a dynamical disorder which lead to a linear density profile.

Estudamos nesta dissertação o conteúdo de operadores da cadeia quântica do modelo XY anisotrópico com interações de três spins (XY triplete anisotrópico). Verificamos que, como no caso de interações de dois spins, este modelo pode ser visto como uma superposição de duas cadeias quânticas Ising, que neste caso apresentam interações de três spins (Ising triplete). Como conseqüência, todo o conteúdo de operadores do modelo XY triplete é obtido através de um estudo sistemático do conteúdo de operadores do Ising triplete o que é feito numericamente explorando-se as relações entre as lacunas de massa e as dimensões anômalas dos operadores do modelo, previstas pela invariância conforme. / We study in this work the operator content of the staggered XY model quantum chain with three-spin interactions (staggered XY triplet). We verified that, as quantum Ising chains, but in this case with three-spin interactions (Ising triplet). It is possible therefore to obtain all the operator content of the XY triplet model by a systematic numerical analysis of the Ising triplet´s operator content, which follows by exploiting the relations between the mass gap amplitudes and the anomalous dimension of the operators of the model, predicted by conformal invariance.

Estudamos nesta dissertação o conteúdo de operadores da cadeia quântica do modelo XY anisotrópico com interações de três spins (XY triplete anisotrópico). Verificamos que, como no caso de interações de dois spins, este modelo pode ser visto como uma superposição de duas cadeias quânticas Ising, que neste caso apresentam interações de três spins (Ising triplete). Como conseqüência, todo o conteúdo de operadores do modelo XY triplete é obtido através de um estudo sistemático do conteúdo de operadores do Ising triplete o que é feito numericamente explorando-se as relações entre as lacunas de massa e as dimensões anômalas dos operadores do modelo, previstas pela invariância conforme. / We study in this work the operator content of the staggered XY model quantum chain with three-spin interactions (staggered XY triplet). We verified that, as quantum Ising chains, but in this case with three-spin interactions (Ising triplet). It is possible therefore to obtain all the operator content of the XY triplet model by a systematic numerical analysis of the Ising triplet´s operator content, which follows by exploiting the relations between the mass gap amplitudes and the anomalous dimension of the operators of the model, predicted by conformal invariance.

Em decorrência do grande avanço alcançado pela mecânica estatística devido a introdução das idéias de invariância conforme às teorias de escala para sistemas finitos, retomamos, neste trabalho, o estudo do modelo XY em campo transverso. A princípio, apresentamos uma análise detalhada do comportamento \"crossover\" característico do modelo, onde incluímos cálculos melhorados dos expoentes da susceptibilidade e do gap de energia anteriormente apresentados por dos Santos e Stinch-combe. Em seguida, uma análise numérica do espectro foi desenvolvida, considerando-se condições livres de contorno, e comparada com as previsões da invariância conforme. Finalmente, as correções à energia do estado fundamental de cadeias finitas foram utilizadas para obter o parâmetro que caracteriza as classes de universalidade (a carga central c). / In view of the great advance attached from statistical mechanics due to the conformal invariance ideas introduced to the scale theories, we take over at this work, the study of the XY model in a transverse field. At first, we present a detailed analysis on the sample\'s typical crossover behavior. An improved calculation of the susceptibility and gap exponents early presented by dos Santos and Stinchcombe is included. Nest, a numerical analysis of the spectrum, regarding free boundary condi¬tions was developed and compared with conformal invariance predictions. Finally, the fundamental state energy corrections of finite chains were used to obtain the parameter which ,distingoishes the universality classes (the central charge c).

Abstract In this study, we employed the Monte Carlo simulation method to investigate the q-state coupled XY model based on the Landau free energy of couple hexatic order and herringbone order proposed by Bruinsma and Aeppli. On two-dimensional triangular lattices simulation results reveal that the q-state coupled XY model will generate a q-state clock phase transition and a XY transition. The unique generated q-state clock phase transition and XY transition will couple in some coupling parameter domain. The novel coupled transitions behavior agree with the phase transition of some kinds of liquid crystal. For example, the three-state Potts phase transition generated by a 3-state coupled XY model and the Sm-A ¡÷Hex-B transition of free ¡V standing two layers liquid crystal are matched. Their heat capacity anomaly is similar and the heat capacity exponent is both closed to £\¡Ü0.3. We also investigated the system of coupled ferromagnetic order and antiferromagnetic order. Adapted the positive coupling parameter on the Hamiltonian of 3-state coupled XY model, the simulation results reveal that the system generate an antiferromagnetic three-state Potts transition. In some parameter domain the antiferromagnetic three-state Potts transition and XY transition are coupled, and become a novel transition. The novel transition may explain the Sm-A ¡÷Hex-B transition of some kinds of liquid crystal which lack herringbone order.