Metastability of non-reversible mean-field Potts model with three spins

TL;DR

This paper investigates the metastable behavior of a non-reversible mean-field Potts model with three spins, identifying critical temperatures, metastable regimes, and effects of external fields through analytical and perturbative methods.

Contribution

It introduces a detailed analysis of metastability in a non-reversible three-spin mean-field Potts model, including effects of external fields, which was not previously explored.

Findings

Identifies three critical temperatures and five metastable regimes.

Extends analysis to small external fields using perturbation.

Demonstrates phenomena unique to large external fields.

Abstract

We examine a non-reversible, mean-field Potts model with three spins on a set with $N\uparrow\infty$ points. Without an external field, there are three critical temperatures and five different metastable regimes. The analysis can be extended by a perturbative argument to the case of small external fields. We illustrate the case of large external fields with some phenomena which are not present in the absence of external field.