Simulations of metastable decay in two- and three-dimensional models with microscopic dynamics

TL;DR

This paper analyzes the decay of metastable phases in lattice-gas models using Monte Carlo simulations, identifying different regimes and crossover points, and applying nucleation theory to interpret the results.

Contribution

It provides a detailed phase diagram and regime classification for metastable decay in 2D and 3D lattice models, with quantitative estimates and theoretical analysis.

Findings

Multiple regimes with distinct functional forms of metastable lifetime

Estimates for crossover points between regimes

Application of Kolmogorov-Johnson-Mehl-Avrami theory to simulation data

Abstract

We present a brief analysis of the crossover phase diagram for the decay of a metastable phase in a simple dynamic lattice-gas model of a two-phase system. We illustrate the nucleation-theoretical analysis with dynamic Monte Carlo simulations of a kinetic Ising lattice gas on square and cubic lattices. We predict several regimes in which the metastable lifetime has different functional forms, and provide estimates for the crossovers between the different regimes. In the multidroplet regime, the Kolmogorov-Johnson-Mehl-Avrami theory for the time dependence of the order-parameter decay and the two-point density correlation function allows extraction of both the order parameter in the metastable phase and the interfacial velocity from the simulation data.