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Doctoral Thesis
Full name
Adriana Brunstein
Knowledge Area
Date of Defense
São Paulo, 1999
Castro, Tania Tome Martins de (President)
Fazzio, Adalberto
Felicio, Jose Roberto Drugowich de
Figueiredo, Wagner
Oliveira, Suzana Maria Moss de
Title in Portuguese
Comportamento Crítico e Transições de Fases Dinâmicas em Autômatos Celulares Probabilísticos
Keywords in Portuguese
Física da matéria condensada
Matéria condensada
Mecânica estatística
Abstract in Portuguese
Estudamos o comportamento crítico e transições de fase em modelos estocásticos irreversíveis, através de simulações numéricas, análise de campo médio e séries perturbativas. Na primeira parte do trabalho, analisamos o comportamento crítico de autômatos celulares irreversíveis, cujas regras dinâmicas são invariantes sob as operações de simetria do grupo C3v. Estudamos as transições de fase dinâmicas que ocorrem nos modelos e obtemos, através de simulações de Monte Carlo, expoentes críticos estáticos e dinâmicos. Nossos resultados indicam que os modelos pertencem a mesma classe de universalidade do modelo de Potts de três estados. Essa conjectura também foi desenvolvida considerando expansões análogas àquelas utilizadas na teoria de Landau de transições de fase. Na segunda parte do trabalho utilizamos o formalismo de operadores como uma forma ele abordar problemas de sistemas ele não-equilíbrio. Aplicamos o formalismo para construir séries perturbativas para modelos irreversíveis ele dois estados.
Title in English
Critical behavior and phase transitions in dynamic probabilistic cellular automata.
Keywords in English
Condensed matter
Condensed matter physics
Statistical mechanics
Abstract in English
We study the critical behavior and phase transitions that take place in irreversible stochastic models through numerical simulations, mean field analysis and perturbative series. In the first part of this work we analyze the critical behavior of irreversible cellular automata whose dynamic rules are invariant under the symmetry operations of the point group C3v. We study the dynamical phase transitions that occur in the models and we obtain the static and dynamic critical exponents by the use of Monte Carlo simulations. Our results indicate that these models are in the same universality class as the three-state Potts model. This conjecture is also developed by considering expansions that are similar to those used in the Landau theory of phase transitions. In the second part of this work we use the operator fonnalism as a way to approach non- equilibrium systems. We apply this fonnalism in order to build perturbative series for two-state irreversible models.
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