The 2D Ising model near criticality: a FK percolation analysis

TL;DR

This paper analyzes the 2D Ising model near critical temperature using FK percolation, providing large deviations estimates related to phase coexistence as the system approaches criticality.

Contribution

It introduces a novel large deviations framework for FK-percolation events in the 2D Ising model near criticality, linking percolation properties to phase coexistence.

Findings

Large deviations estimates for FK-percolation events near criticality

Phase coexistence phenomena characterized close to the critical point

Asymptotic behavior of the model as temperature approaches criticality

Abstract

We study the 2d-Ising model defined on finite boxes at temperatures that are below but very close from the critical point. When the temperature approaches the critical point and the size of the box grows fast enough, we establish large deviations estimates on FK-percolation events that concern the phenomenon of phase coexistence.