Improved Taylor Expansion method in the Ising model

TL;DR

This paper introduces an improved variational Taylor expansion method for the 2D Ising model, allowing accurate evaluation of free energy and magnetization in strong coupling regions and near phase transitions.

Contribution

The paper presents a novel variational Taylor expansion approach that extends the applicability of weak coupling expansions to strong coupling and phase transition regions in the Ising model.

Findings

Successfully estimates the transition point.

Identifies stable and metastable states under magnetic fields.

Applicable to phase transition analysis.

Abstract

We apply an improved Taylor expansion method, which is a variational scheme to the Ising model in two dimensions. This method enables us to evaluate the free energy and magnetization in strong coupling regions from the weak coupling expansion, even in the case of a phase transition. We determine the approximate value of the transition point using this scheme. In the presence of an external magnetic field, we find both stable and metastable physical states.