Simulações entrópicas do modelo de Ashkin-Teller

• Autor(a) principal: Ferreira, Lucas de Souza
• Data de Publicação: 2016
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• dARK ID: ark:/38995/0013000004k4p
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/6325
• topic: Ashkin-Teller; Simulações entrópicas; Wang-Landau; Transições de fases; Entropic simulation; Phase transition; FISICA::FISICA GERAL

In 1943, Ashkin and Teller (AT) proposed a model to describe the behavior of a system composed by four components that interact with each other. However the problem has not been solved analytically for all parameters due to the complexity of the model. Only thirty years later Fan (1972) proposed a change in order to analyze the system. He made an analogy with the Ising model and described the interactions between the components in terms of spins, leading to a simple matching with the Ising and Potts q = 4 models and, enabling therefore a clearer comprehension of the model and allowing the implementation of various techniques to investigate the behavior of the system with the temperature. In 2001 Wang and Landau developed a Monte Carlo algorithm that estimates directly the density of states and can be applied in the study of phase transitions and the thermodynamic properties. This algorithm is based on a random walk in the space of energies that leads to an estimate for the density of states. During the simulations an energy histogram monitors the evolution of the density of states: whenever the flatness criterion is satisfied, we obtain a finer level of the density of states. In this work we perform a study of the Ashkin-Teller model using the Wang-Landau algorithm, determining the behavior of the magnetization and the specific heat and estimating the critical exponents , and and the critical temperature through the finite-size theory for different values of the model parameters.