Pirogov-Sinai Theory With New Contours for Symmetric Models

TL;DR

This paper introduces a new contour definition in Pirogov-Sinai theory that simplifies applying Peierls argument to symmetric models, broadening the theory's applicability.

Contribution

A novel contour definition enabling easier proof of Pirogov-Sinai results for symmetric models using Peierls argument.

Findings

New contours facilitate classical Peierls argument application.

Simplified proof structure for symmetric models.

Enhanced theoretical framework for phase transition analysis.

Abstract

The contour argument was introduced by Peierls for two dimensional Ising model. Peierls benefited from the particular symmetries of the Ising model. For non-symmetric models the argument was developed by Pirogov and Sinai. It is very general and rather difficult. Intuitively clear that the Peierls argument does work for any symmetric model. But contours defined in Pirogov-Sinai theory do not work if one wants to use Peierls argument for more general symmetric models. We give a new definition of contour which allows relatively easier prove the main result of the Pirogov-Sinai theory for symmetric models. Namely, our contours allow us to apply the classical Peierls argument (with contour removal operation).