Stability of uniqueness and coexistence of equilibrium states of the Ising model under long range perturbations

TL;DR

This paper investigates how long-range perturbations affect the stability of equilibrium states in the high and low temperature regimes of the d-dimensional Ising model, demonstrating that certain properties are preserved under symmetric perturbations.

Contribution

It establishes the stability of uniqueness and coexistence of equilibrium states in the Ising model under long-range, spin-flip symmetric perturbations, extending previous results beyond Pirogov-Sinai theory.

Findings

Uniqueness at high temperature is preserved under perturbations.

Coexistence at low temperature remains stable with symmetric perturbations.

Results extend understanding of phase stability in long-range interacting systems.

Abstract

In this paper, we study perturbations of the $d$-dimensional Ising model for $d\geq 2$, including long range ones to which the Pirogov-Sinai theory is not applicable. We show that the uniqueness of the equilibrium state of the Ising model at high temperature and the coexistence of equilibrium states at low temperature are preserved by spin-flip symmetric perturbations.