Metastability of the two-dimentional Blume-Capel model with zero chemical potential and small magnetic field on a large torus

TL;DR

This paper analyzes the metastable behavior of the two-dimensional Blume-Capel model with zero chemical potential and a small magnetic field, demonstrating the transition pathways between different spin configurations on a large torus.

Contribution

It provides a rigorous proof of metastability and describes the transition process from negative spins to the ground state in this specific model.

Findings

Proves metastable behavior in the model.

Shows the transition from negative to zero spins.

Identifies the ground state as all +1 spins.

Abstract

We consider the Blume-Capel model with zero chemical potential and small magnetic field in a two-dimensional torus whose length increaseswith the inverse of the temeprature. We prove the mestastable behavior and that starting from a configuration with only negative spins, the process visits the configuration with only 0-spins on its way to the ground state which is the configuration with all spins equal to +1.