Monte Carlo dinâmico aplicado aos modelos de Ising e Baxter-Wu.

Abstract

Short-time simulations have been used with great frequency in the literature. That technique was discovered by Li, Shulke and Zheng that, inspired in previous works by Huse and Janssen et al., showed that generalizations of quantities like magnetization and the Binder s cumulant exhibit universal behavior in the beginning of the simulation (early time behavior). The study of criticality in short-times provides an alternative way to estimate the dynamic critical exponent z, besides allowing the calculation of a new dynamic exponent ?, associated to the anomalous behavior of the magnetization. In the same way, time-dependent simulations became a useful tool to study phase transitions in cellular automata and also for spin models. In fact, the best estimates for the exponent z of the two-dimensional Ising model were obtained through the technique of damage spreading, introduced by Kauffman in the study of cellular automata, later widespread for spin models. In the first part of this work we used short-time Monte Carlo simulations to investigate the Baxter-Wu model, defined in a triangular lattice whose variables are Ising-like coupled by triplet interactions. We have obtained estimates for the dynamic critical exponents z and ? besides static exponents β e ν. Our results do not corroborate recent estimates by Santos and Figueiredo for the critical exponent z. In the second part of this work, we investigated the damage spreading in the one-dimensional Ising model under two dynamics introduced by Hinrichsen and Domany (HD). In particular, we study the effects of synchronous (parallel) and asynchronous (continuous dynamics) updating on the spreading properties. We showed that the damage does not spread when the second dynamic is implemented in an asynchronous way. We found that the rules for updating the damage produced by this dynamic, as the temperature goes to infinity and a certain parameter λ is zero, are equivalent to those of Grassberger’s wellknown model A cellular automaton. A minha Mae, ao Kioshi e ao meu Avo pelo apoio em todos esses anos