Low-temperature Metastability of Ising Models: Prefactors, Divergences, and Discontinuities

TL;DR

This paper investigates the low-temperature metastability of Ising models, focusing on how prefactors, divergences, and discontinuities affect the validity of theoretical results, using advanced Monte Carlo simulations.

Contribution

It provides a detailed analysis of the conditions under which low-temperature theoretical results for Ising models are valid, highlighting the roles of prefactors and critical fields.

Findings

Prefactors exhibit discontinuities and divergences near certain fields.

The validity of low-temperature results depends on the system's proximity to these critical fields.

Monte Carlo simulations confirm the theoretical predictions about metastable lifetimes.

Abstract

The metastable lifetime of the square-lattice and simple-cubic-lattice kinetic Ising models are studied in the low-temperature limit. The simulations are performed using Monte Carlo with Absorbing Markov Chain algorithms to simulate extremely long low-temperature lifetimes. The question being addressed is at what temperatures the mathematically rigorous low-temperature results become valid. It is shown that the answer depends partly on how close the system is to fields at which the prefactor for the metastable decay either has a discontinuity or diverges.