Metastability of Blume-Capel model with zero chemical potential and zero external field

TL;DR

This paper analyzes the metastable behavior of the Blume-Capel model with zero chemical potential and external field at low temperatures, revealing a flat energy landscape with no critical configurations.

Contribution

It provides a detailed potential-theoretic and large deviation analysis of metastability in this specific Blume-Capel model setting, highlighting the flat energy landscape structure.

Findings

No critical configurations exist in the energy landscape.

A flat plateau of saddle configurations is present.

Metastable behavior characterized by large deviations and potential theory.

Abstract

In this study, we investigate the metastable behavior of Metropolis-type Glauber dynamics associated with the Blume-Capel model with zero chemical potential and zero external field at very low temperatures. The corresponding analyses for the same model with zero chemical potential and positive small external field were performed in [Cirillo and Nardi, Journal of Statistical Physics, 150: 1080-1114, 2013] and [Landim and Lemire, Journal of Statistical Physics, 164: 346-376, 2016]. We obtain both large deviation-type and potential-theoretic results on the metastable behavior in our setting. To this end, we perform highly thorough investigation on the energy landscape, where it is revealed that no critical configurations exist and alternatively a massive flat plateau of saddle configurations resides therein.