Estudo numerico de modelos dinamicos em fisica estatistica com invariancia de escala

Abstract

In this thesis, three types models of statistical physics are studied numerically. The first of these are the interface models. These models describe spatially non-homogeneous systems which may not be in thermodynamic equilibrium. The scale invariance properties, together with a continuum description allow a classification of several discrete models in universality classes. Results of Monte-Carlo simulations for an interface in the extremely anisotropic two-dimensional Ising model are presented. The study of the properties of the center of mass of the interface, in this model, shows that one can differentiate interfaces in equilibrium from, the non-equilibrium ones by numerical estimates of the exponents. The usefulness of the analysis, based on the center of mass properties, is demonstrated for an SOS model, in two and three dimensions. Moreover, the difference in the scaling behaviour of the variance of the center of mass with the system size for equilibrium and non-equilibrium is interpreted as a breakdown of the central limit theorem. The second type of models consists of models with absorbing states. these are non-equilibrium models and they show a phase transition for dimensions greater than or equal to one. This phase transition is studied, for a one dimensional model, by solving numerically the corresponding master equation. Several mean-field approximations are considered, and it is shown that despite the approximate nature of the method the critical exponents can be obtained with reasonable accuracy by considering systems of increasing size. The results agree with the ones expected for the universality class of the model. The usefulness of the method is further shown by studying a model where long range interactions are present. Considering variable range interactions it is possible to identify the regimes corresponding to the short-range and the mean-field exponents. The extension of the method to two-dimensional systems is also considered. Here, the Monte-Carlo method is needed for sampling the corresponding stochastic process. The third and the last category of models consists of models of continuous spins such as the #phi#"4 model and Gaussian model..Available from Fundacao para a Ciencia e a Tecnologia, Servico de Informacao e Documentacao, Av. D. Carlos I, 126, 1200 Lisboa / FCT - Fundação para o Ciência e a TecnologiaSIGLEPTPortuga