Exploring Metastability in Ising models: critical droplets, energy barriers and exit time

TL;DR

This paper reviews the metastable behavior of the Ising model, focusing on transition times, critical configurations, and energy barriers across various contexts and related models, under different dynamics.

Contribution

It provides a comprehensive overview of metastability in the Ising model and extends the analysis to related models and dynamics, highlighting critical configurations and energy barriers.

Findings

Identification of critical configurations during transitions

Calculation of energy barriers for metastable to stable states

Analysis of metastability across different models and dynamics

Abstract

This paper provides an overview of the research on the metastable behavior of the Ising model. We analyze the transition times from the set of metastable states to the set of the stable states by identifying the critical configurations that the system crosses with high probability during this transition and by computing the energy barrier that the system must overcome to reach the stable state starting from the metastable one. We describe the dynamical phase transition of the Ising model evolving under Glauber dynamics across various contexts, including different lattices, dimensions and anisotropic variants. The analysis is extended to related models, such as long-range Ising model, Blume-Capel and Potts models, as well as to dynamics like Kawasaki dynamics, providing insights into metastability across different systems.