Estudamos vários modelos de polímeros (Caminhadas auto- e mutuamente excludentes sobre redes) que apresentam pontos tricríticos em seus diagramas de fases. Concentramos a nossa atenção nos problemas de polímeros com interações atrativas, nos quais o ponto tricrítico é conhecido como ponto H na literatura, e de polímeros na presença de diluição recozida. Analisamos o comportamento termodinâmico desses modelos na rede de Bethe e em gaxetas de Sierpinski bi- e tridimensionais, bem como na rede quadrada. Nas redes de Bethe e fractais foi possível obter soluções exatas. Já na rede quadrada empregamos métodos baseados na teoria de escala para sistemas finitos através do cálculo da matriz de transferência. Enfatizamos o estudo dos pontos tricríticos, dando particular atenção ao cálculo de seus expoentes nas redes fractais e quadrada. Na rede de Bethe, onde os expoentes são clássicos, foi possível estudar em detalhe o diagrama de fases do modelo com diluição e interações atrativas. / We study several polymer models (self- and mutually avoiding walks on lattices) which display tricritical points in their phase diagrams. We concentrated our attention on the problems of polymers with attrative interactions, where the tricritical point is known as H point in the literature, and of polymers in the presence of annealed dilution. We considered the thermodynamic behavior of these models on the Bethe lattice, on the two- and three-dimentional Sierpinski gaskets, and on the square lattice. On the Bethe and the Sierpinski gaskets an exact solution could be obtained. On the square lattice we used finite size scaling methods together with transfer matrix calculations. We stressed the study of the tricritical points, paying particular attention to the calculation of their exponents on the fractal and the square lattice. On the Bethe lattice, where the exponents are classical, it was possible to study in detail the phase diagram of the model with dilution and attractive interactions.

Estudamos vários modelos de polímeros (Caminhadas auto- e mutuamente excludentes sobre redes) que apresentam pontos tricríticos em seus diagramas de fases. Concentramos a nossa atenção nos problemas de polímeros com interações atrativas, nos quais o ponto tricrítico é conhecido como ponto H na literatura, e de polímeros na presença de diluição recozida. Analisamos o comportamento termodinâmico desses modelos na rede de Bethe e em gaxetas de Sierpinski bi- e tridimensionais, bem como na rede quadrada. Nas redes de Bethe e fractais foi possível obter soluções exatas. Já na rede quadrada empregamos métodos baseados na teoria de escala para sistemas finitos através do cálculo da matriz de transferência. Enfatizamos o estudo dos pontos tricríticos, dando particular atenção ao cálculo de seus expoentes nas redes fractais e quadrada. Na rede de Bethe, onde os expoentes são clássicos, foi possível estudar em detalhe o diagrama de fases do modelo com diluição e interações atrativas. / We study several polymer models (self- and mutually avoiding walks on lattices) which display tricritical points in their phase diagrams. We concentrated our attention on the problems of polymers with attrative interactions, where the tricritical point is known as H point in the literature, and of polymers in the presence of annealed dilution. We considered the thermodynamic behavior of these models on the Bethe lattice, on the two- and three-dimentional Sierpinski gaskets, and on the square lattice. On the Bethe and the Sierpinski gaskets an exact solution could be obtained. On the square lattice we used finite size scaling methods together with transfer matrix calculations. We stressed the study of the tricritical points, paying particular attention to the calculation of their exponents on the fractal and the square lattice. On the Bethe lattice, where the exponents are classical, it was possible to study in detail the phase diagram of the model with dilution and attractive interactions.

Typescript (photocopy). / Digitized by Kansas Correctional Industries

xiii, 110 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / This dissertation investigates the interplay between, and the possible coexistence of, magnetic and superconducting order in metals. We start with studying the electromagnetic properties of s-wave superconductors near a ferromagnetic instability. By using a generalized Ginzburg-Landau theory and scaling arguments, we show that competition between magnetic order and superconducting order can change the scaling of observables. For instance, the exponent for the temperature dependence of the critical current can deviate from the Ginzburg-Landau value of 3/2. These results may be relevant to understanding the observed behavior of MgCNi 3 . We then study the nature of the superconductor-to-normal-metal transition in p-wave superconductors. Although the phase transition is continuous at a mean- field level, a more careful renormalization-group analysis in conjunction with large-n expansion techniques strongly suggest that the transition is first order. This conclusion is the same as for s-wave superconductors, where these techniques also predict a first-order transition. In p-wave superconductors, topological excitations known as skyrmions are known to exist in addition to the more common vortices. In the third part of this dissertation, we study the properties of skyrmion lattices in an external magnetic field. We propose iv experiments to distinguish vortex lattices from skyrmion lattices by means of their melting curves and their μSR signatures. / Adviser: Dietrich Belitz

Made available in DSpace on 2018-07-27T18:26:04Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-05-08. Added 1 bitstream(s) on 2018-07-27T18:30:08Z : No. of bitstreams: 1 000857175.pdf: 1812316 bytes, checksum: c69f0ce283642ad007739e19ff3a1f71 (MD5) / Estudamos a evolução temporal de parâmetros de ordem conservados e não conservados empregando o formalismo das equações cinéticas semi-fenomenológicas de Ginzburg-Landau-Langevin da teoria clássica das transições de fase dinâmicas. Apresentamos uma aplicação do formalismo ao problema do desconfinamento de quarks e glúons na QCD, em que o parâmetro de ordem conservado é a densidade bariônica e o parâmetro de ordem não conservado é o loop de Polyakov. As equações cinéticas são resolvidas numericamente empregando um esquema semi-implícito no tempo e um método de diferenças finitas com transformada de Fourier rápida para as coordenadas espaciais. Resultados de simulações numéricas são apresentados para valores médios dos parâmetros de ordem e para as funções de estrutura / We study the time evolution of conserved and nonconserved order parameters employing the formalism of the semiphenomenological Ginzburg-Landau-Langevin kinetic equations of the classical theory of dynamical phase transitions. We present an application of the formalism to the deconfinement problem of quarks and gluons in QCD, where the conserved order parameter is the baryon density and the non-conserved order parameter is the Polyakov loop. The kinetic equations are solved numerically employing a semi-implicit scheme for the time variable and a finite-difference method with fast Fourier transform for the space coordinates. Results of the numerical simulations are presented for the average values and structure functions of the order parameters

Nesta dissertação, realizamos um estudo sobre cadeias unidimensionais quânticas de spin meio e spin um exatamente integráveis. Estudamos as propriedades do espectro de energia e efeitos produzidos no mesmo devido à finitude da cadeia. Para tal fim, exploramos as propriedades advindas da invariância por transformações conforme dos modelos em seus respectivos pontos críticos. Como apreciação dessa abordagem, estudamos o modelo exatamente integrável NDF, proposto por Alcaraz e Bariev, para partículas de spin 1. Verificamos em tal modelo uma transição de fase quântica. / In this dissertation, we have studied exactly integrable unidimensional quantum spin chains of spin 1/2 and spin 1. Special atention was given to the properties of the energy eigenspectra of these chains and particularly to their finite size effects. To achieve this goal, we have explored the invariance by conformal transformations of the models in their critical points. As an appreciation of these studies, we have studied the exactly integrable model NDF of spin 1, proposed by Alcaraz e Bariev. We verified that such model possess a quantum phase transition.

Orientador: Gastão Inácio Krein / Banca: Eduardo de Souza Fraga / Banca: Roberto André Kraenkel / Resumo: Estudamos a evolução temporal de parâmetros de ordem conservados e não conservados empregando o formalismo das equações cinéticas semi-fenomenológicas de Ginzburg-Landau-Langevin da teoria clássica das transições de fase dinâmicas. Apresentamos uma aplicação do formalismo ao problema do desconfinamento de quarks e glúons na QCD, em que o parâmetro de ordem conservado é a densidade bariônica e o parâmetro de ordem não conservado é o loop de Polyakov. As equações cinéticas são resolvidas numericamente empregando um esquema semi-implícito no tempo e um método de diferenças finitas com transformada de Fourier rápida para as coordenadas espaciais. Resultados de simulações numéricas são apresentados para valores médios dos parâmetros de ordem e para as funções de estrutura / Abstract: We study the time evolution of conserved and nonconserved order parameters employing the formalism of the semiphenomenological Ginzburg-Landau-Langevin kinetic equations of the classical theory of dynamical phase transitions. We present an application of the formalism to the deconfinement problem of quarks and gluons in QCD, where the conserved order parameter is the baryon density and the non-conserved order parameter is the Polyakov loop. The kinetic equations are solved numerically employing a semi-implicit scheme for the time variable and a finite-difference method with fast Fourier transform for the space coordinates. Results of the numerical simulations are presented for the average values and structure functions of the order parameters / Mestre

In this dissertation, I study critical phenomena and phase transitions in systems with long-range interactions, in particular, the ferromagnetic Ising model with quenched site dilution and the asset exchange model with growth. In the site-diluted Ising model, I focus on the effects of quenched disorder on both critical phenomena and nucleation. For critical phenomena, I generalize the Harris criterion for the mean-field critical point and the spinodal, and find that they are not affected by dilution, whereas pseudospinodals are smeared out. For nucleation, I find that dilution reduces the lifetime of the metastable state. I also investigate the structure of nucleating droplets in both nearest-neighbor and long-range Ising models. In both cases, nucleating droplets are more likely to occur in spatially more dilute regions. I also modify the asset exchange model to include different types of economic growth, such as constant growth and geometric growth. For constant growth, one agent eventually gets almost all the wealth regardless of the growth rate. For geometric growth, the wealth distribution depends on the way that the growth is distributed among agents, which is represented by the parameter 𝛾. For the evenly distributed growth, 𝛾=0, and as 𝛾 increases, the growth in the total wealth is distributed preferentially to richer agents. For 𝛾=1, the wealth of every agent grows at a rate that is linearly proportional to his/her wealth. I find a phase transition at 𝛾=1. For 𝛾<1, there is an rescaled steady state wealth distribution and the system is effectively ergodic. In this state, the wealth at all ranks grows exponentially in time and inequality stays constant. For 𝛾>1, one agent eventually obtains almost all the wealth, and the system is not ergodic. For 𝛾=1$, the dynamics of the poor agents' wealth is similar to that of a geometric random walk. In addition, I elucidate the effects of unfair trading, inhomogeneity in agents, modified growth which only depends on richest $1% agents' wealth, and a finite range of wealth exchange.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第23452号 / 理博第4746号 / 新制||理||1680(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 松田 祐司, 教授 石田 憲二, 教授 柳瀬 陽一 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18777号 / 理博第4035号 / 新制||理||1581(附属図書館) / 31728 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 石田 憲二, 教授 田中 耕一郎, 教授 前野 悦輝 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM