Phase diagram for the antiferromagnetic Blume-Capel model near tricriticality.

Abstract

We study the two-dimensional, antiferromagnetic Blume-Capel model on a square lattice by numerical transfer-matrix and Monte Carlo finite-size scaling methods, in order to investigate whether the line of tricritical points in this model may be decomposed into lines of critical end points and double critical points, as predicted by mean-field theory and recent Monte Carlo simulations on a three-dimensional cubic lattice. Conclusive numerical evidence is obtained, indicating that such decomposition does u/Inot occur in this two-dimensional model. The nondecomposition is explained in terms of the large fluctuations in the two-dimensional nearest-neighbor model, and we speculate that the situation may be different in two-dimensional antiferromagnetic models with weak, ferromagnetic next-nearest-neighbor interactions.