Multiphase structure of finite-temperature phase diagram of the Blume-Capel model. Wang-Landau sampling method

TL;DR

This paper explores the finite-temperature phase diagram of the Blume-Capel model using Wang-Landau sampling to precisely estimate the density of states, revealing multicritical behavior and phase coexistence in an antiferromagnetic spin system.

Contribution

It introduces an efficient Wang-Landau sampling approach to analyze the phase structure and phase coexistence in the Blume-Capel model at finite temperatures.

Findings

Identification of multicritical points and phase boundaries.

Observation of coexistence of antiferromagnetic phases.

Precise thermodynamic calculations using DOS estimation.

Abstract

We investigate the density of states (DOS) in an antiferromagnetic spin-system on a square lattice described by the Blume-Capel (BC) model. We use a new and very efficient simulation method, proposed by Wang and Landau, in which we estimate very precisely DOS by sampling in the space of energy. Then we calculate the thermodynamical averages like internal energy, free energy, specific heat and entropy. The BC model exhibits multicritical behaviour such as first- or second-order transitions and tricritical points. It is known that the ground state of the model can exhibit two kinds of staggered antiferromagnetic phases: AF1 (two interpenetrating lattices with S = -1 and S = 1) and AF2 (S = -1 and S = 0 for H < 0; S = 1 and S = 0 for H > 0). We analyze the coexistence of such phases at finite temperatures and determine border lines between them. To understand the microscopic nature of such boundaries we present also some results obtained with the standard Monte Carlo method.