Metastability of reversible finite state Markov processes

TL;DR

This paper establishes the conditions under which reversible finite state Markov processes exhibit metastability, and demonstrates this behavior in the low-temperature Ising model with a small magnetic field.

Contribution

It provides a minimal-condition proof of metastability in reversible Markov processes and applies it to the Ising model at low temperature.

Findings

Reversible Markov processes show metastability under minimal conditions.

Metastable behavior is demonstrated in the low-temperature Ising model.

Theoretical framework for metastability in finite state spaces.

Abstract

We prove the metastable behavior of reversible Markov processes on finite state spaces under minimal conditions on the jump rates. To illustrate the result we deduce the metastable behavior of the Ising model with a small magnetic field at very low temperature.