Metastability of the two-dimensional Blume-Capel model with zero chemical potential and small magnetic field

TL;DR

This paper investigates the metastable behavior of the two-dimensional Blume-Capel model with zero chemical potential and small magnetic field, providing precise transition time estimates and characterizing critical configurations at low temperatures.

Contribution

It offers the first sharp estimates for transition times and a detailed characterization of critical configurations in this specific metastable system.

Findings

Sharp estimates for transition times

Characterization of critical configurations

Proof of metastable behavior at low temperatures

Abstract

We consider the two-dimensional Blume-Capel model with zero chemical potential and small magnetic field evolving on a large but finite torus. We obtain sharp estimates for the transition time, we characterize the set of critical configurations, and we prove the metastable behavior of the dynamics as the temperature vanishes.