Estudo de campo médio do modelo de Blume-Capel Spin-2

Abstract

In this work we study the Spin-2 Blume-Capel model by using the Bogoliubov variational principle, also known as Gibbs-Bogoliubov inequality. In order to learn the method, we first applied it to the Spin-1/2 Ising model. Then, both the Spin-1 and Spin-2 BlumeCapel models were treated. From the minimization of a specific function with respect to its variational parameters, one can evaluate physical quantities such as magnetization, partition function, Gibbs free energy, and quadrupole moment. The phase diagrams of the Blume-Capel models (Spin-1 and Spin-2) were obtained and both include discontinuous and continuous transitions, separated by tricritical points. The transition lines and the tricritical points were also computed from the coefficients of the Landau free energy series expansion at zero external field.