Metastability for the Ising Model on the hypercube

TL;DR

This paper analyzes the metastable behavior of the low-temperature Ising model on an n-dimensional hypercube, providing precise asymptotic estimates for the crossover time between two uniform configurations as temperature approaches zero.

Contribution

It offers the first detailed asymptotic analysis of the crossover time for the Ising model on the hypercube at low temperatures, extending understanding of metastability in high-dimensional structures.

Findings

Derived precise asymptotics for crossover time as temperature approaches zero.

Identified the dominant configurations and transition pathways in the hypercube.

Quantified the metastable transition times in high-dimensional settings.

Abstract

We consider Glauber dynamics for the low-temperature, ferromagnetic Ising Model set on the n-dimensional hypercube. We derive precise asymptotic results for the crossover time (the time it takes for the dynamics to go from the configuration with a "-1" at every vertex, to the configuration with a "+1" at each vertex) in the limit as the inverse temperature $\beta\rightarrow\infty$.