A mean-field approach applied for the ferromagnetic spin-1 Blume-Capel model

TL;DR

This paper introduces a novel mean-field Monte Carlo method to study the phase diagram and thermodynamic properties of the spin-1 ferromagnetic Blume-Capel model on square and linear lattices, improving accuracy over traditional methods.

Contribution

The paper presents the MFT-MC approach, combining mean-field theory with Monte Carlo simulations, to better analyze phase transitions in the Blume-Capel model.

Findings

Qualitative phase diagram consistent with expected behavior

First-order line correctly perpendicular to anisotropy axis at low temperatures

Thermodynamic quantities like entropy and specific heat analyzed

Abstract

We applied a mean-field approach associated to Monte Carlo simulations in order to study the spin-1 ferromagnetic Blume-Capel model in the square and the linear lattice. This new technique, which we call MFT-MC, determines the molecular field as the magnetization response of a Monte Carlo simulation. The resulting phase diagram is qualitatively correct, in contrast to effective-field approximations, in which the first-order line is not perpendicular to the anisotropy axis at low temperatures. Thermodynamic quantities, as the entropy and the specific heat curves can be obtained so as to analyze the nature of the phase transition points. Also, the possibility of using larger sizes constitutes an improvement regarding other mean-field approximations that use clusters.