Approaching equilibrium and the distribution of clusters

Abstract

We investigate the approach to stable and metastable equilibrium in Ising models using a cluster representation. The distribution of nucleation times is determined using the Metropolis algorithm and the corresponding ${\varphi }^4$ model using Langevin dynamics. We find that the nucleation rate is suppressed at early times even after global variables such as the magnetization and energy have apparently reached their time independent values. The mean number of clusters whose size is comparable to the size of the nucleating droplet becomes time independent at about the same time that the nucleation rate reaches its constant value. We also find subtle structural differences between the nucleating droplets formed before and after apparent metastable equilibrium has been established.

22 pages, 16 figures

References in corpus (6)

• Monte Carlo computation of correlation times of independent relaxation modes at criticality
• Medium-range interactions and crossover to classical critical behavior
• The structure of fluctuations near mean-field critical points and spinodals and its implication for physical processes
• Large-scale Simulation of the Two-dimensional Kinetic Ising Model
• Transient Nucleation near the Mean-Field Spinodal
• Evidence for sharper than expected transition between metastable and unstable states