Relaxation Height in Energy Landscapes: an Application to Multiple Metastable States

TL;DR

This paper introduces the concept of relaxation height in energy landscapes with multiple metastable states, providing conditions to analyze such systems and applying the theory to the Blume--Capel model.

Contribution

It develops a general framework for understanding relaxation heights in complex energy landscapes with multiple metastable states and demonstrates its application to a specific statistical physics model.

Findings

Established sufficient conditions for relaxation height in multiple metastable states

Applied the theory to the Blume--Capel model with two metastable states

Provided insights into the mathematical structure of systems with multiple metastable states

Abstract

The study of systems with multiple (not necessarily degenerate) metastable states presents subtle difficulties from the mathematical point of view related to the variational problem that has to be solved in these cases. We introduce the notion of relaxation height in a general energy landscape and we prove sufficient conditions which are valid even in presence of multiple metastable states. We show how these results can be used to approach the problem of multiple metastable states via the use of the modern theories of metastability. We finally apply these general results to the Blume--Capel model for a particular choice of the parameters ensuring the existence of two multiple, and not degenerate in energy, metastable states.