Metastable lifetimes in a kinetic Ising model: Dependence on field and system size

TL;DR

This study investigates how the lifetimes of metastable states in kinetic Ising models depend on external field strength and system size, using droplet theory and Monte Carlo simulations to identify universal behaviors and regime transitions.

Contribution

It provides a quantitative verification of droplet theory predictions for metastable lifetimes and characterizes different field regimes and their effects on decay dynamics.

Findings

Lifetimes follow an exponential inverse field dependence with universal and nonuniversal factors.

Four distinct field regimes with different lifetime behaviors are identified.

The crossover field between regimes decreases logarithmically with system size.

Abstract

The lifetimes of metastable states in kinetic Ising ferromagnets are studied by droplet theory and Monte Carlo simulation, in order to determine their dependences on applied field and system size. For a wide range of fields, the dominant field dependence is universal for local dynamics and has the form of an exponential in the inverse field, modified by universal and nonuniversal power-law prefactors. Quantitative droplet-theory predictions are numerically verified, and small deviations are shown to depend nonuniversally on the details of the dynamics. We identify four distinct field intervals in which the field dependence and statistical properties of the lifetimes are different. The field marking the crossover between the weak-field regime, in which the decay is dominated by a single droplet, and the intermediate-field regime, in which it is dominated by a finite droplet density, vanishes logarithmically with system size. As a consequence the slow decay characteristic of the former regime may be observable in systems that are macroscopic as far as their equilibrium properties are concerned.