Simulações entrópicas do Modelo de Baxter-Wu

• Autor(a) principal: Jorge, Lucas Nunes
• Data de Publicação: 2017
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/7777
• topic: Amostragem entrópica; Modelo de Baxter-Wu; Classe de universalidade; Temperatura crítica; Entropic sampling; Baxter-Wu Model; Universality class; Critical temperature; FISICA GERAL::FISICA ESTATISTICA E TERMODINAMICA

In this work, we used a refined entropy sampling technique based on the Wang- Landau method and finite-size scaling techniques to study variations of the Baxter-Wu model, namely: spin-$1/2$, spin-$1$, spin-$1$ with the crystal field interaction and was done a three-dimensional proposal for the model. It was also verified characteristics in the order parameter to be adopted in the simulations. The universality class and the critical temperature were calculated for the spin-$1/2$ case, and the results founded were in good agreement with the exact ones found in the literature. We sought to determine the kind of the phase transition that the model suffers for the spin-$1$ case, being carried out a detailed study for continuous and discontinuous phase transitions. The Baxter-Wu model with crystal field, $D$, had its phase diagram constructed, as well as the determination of the point at which discontinuous transitions finalizes. The critical exponent, $\nu$, was evaluated for several values of the crystal field, where we verified is variation along the critical line, with the existence of a peak, corroborating the existence of a multicritic behavior of the model. We also observed the existence of an anomaly in the specific heat, associated to the Schottky defect. This anomaly appears more clearly for values of $D \geq 1.990$. In the study of the order parameter, we verified that in the simulations one should not, when considering lattice sizes multiple of three, use the order parameter as the total magnetization of the lattice, but to consider the magnetization by sub-lattices. When working with sizes of lattices that are not multiples of three, it is not a problem to adopt the order parameter as the total magnetization of the lattice. A three-dimensional proposal was also made for the Baxter-Wu model, and its phase transition was characterized.