Field theoretical approach to spin models

TL;DR

This paper introduces a non-perturbative, field-theoretical approach using Dyson-Schwinger and $\

Contribution

It presents a systematic method to analyze Ising models beyond mean field theory, accurately predicting critical temperatures and correlations.

Findings

Critical temperature closely matches other non-cluster methods.

Green function spectrum becomes gapless at critical point.

Susceptibility diverges at Tc, indicating phase transition.

Abstract

We developed a systematic non-perturbative method base on Dyson-Schwinger theory and the $\Phi$-derivable theory for Ising model at broken phase. Based on these methods, we obtain critical temperature and spin spin correlation beyond mean field theory. The spectrum of Green function obtained from our methods become gapless at critical point, so the susceptibility become divergent at Tc. The critical temperature of Ising model obtained from this method is fairly good in comparison with other non-cluster methods. It is straightforward to extend this method to more complicate spin models for example with continue symmetry.