Modelo de Baxter-Wu em uma, duas e três dimensões para spin 1/2

Abstract

This work consists in investigating the phases and transition between them in a magnetic model, namely the Baxter-Wu (B-W) model, in different spatial dimensions. Although the model was originally proposed for a two-dimensional triangular lattice, we will here make a generalization for one- and three-dimensional lattices as well. In one-dimension, the model can be treated by means of the transfer matrix technique. Although it is an exact procedure, in which the system does not present any phase transition, the results can not be written in a closed analytical form for non-zero external field, and are given by the eigenvalues of a non-Hermitian matrix. For zero external field, the partition function is calculated. In two and three dimensions the model is studied using the Mean Field Theory (MFT), using the scheme based on the Bogoliubov inequality. In this treatment, we use blocks of a single spin, a triangle of spins, and in two and three dimensions the exact results for the one-dimensional network. Although the values of the transition temperature are close to the expected values for each lattice, the transition is always of first order, whereas the exact results for the two-dimensional triangular lattice confirm a second-order transition.