On the uniqueness of Gibbs states in the Pirogov-Sinai theory

TL;DR

This paper proves that in low-temperature systems within Pirogov-Sinai theory, if translation-periodic Gibbs states are unique, then no other Gibbs states exist, with an exponential convergence rate to this state.

Contribution

It establishes that local uniqueness of translation-periodic Gibbs states implies global uniqueness in low-temperature Pirogov-Sinai systems.

Findings

Uniqueness of translation-periodic Gibbs states implies global uniqueness.

Exponential rate of convergence to the infinite volume state.

No existence of non-periodic Gibbs states under the given conditions.

Abstract

We prove that, for low-temperature systems considered in the Pirogov-Sinai theory, uniqueness in the class of translation-periodic Gibbs states implies global uniqueness, i.e. the absence of any non-periodic Gibbs state. The approach to this infinite volume state is exponentially fast.