Investigation of metastable states and nucleation in the kinetic Ising model

Abstract

The relaxation of a two-dimensional Ising ferromagnet after a sudden reversal of the applied magnetic field is studied from various points of view, including nucleation theories, computer experiments, and a scaling theory, to provide a description for the metastable states and the kinetics of the magnetization reversal. Metastable states are characterized by a "flatness" property of the relaxation function. The Monte Carlo method is used to simulate the relaxation process for finite $L\ifmmode\times\else\texttimes\fi{}L$ square lattices ($L=55, 110, 220 \mathrm{and} 440, \mathrm{respectively}$); no dependence on $L$ is found for these systems in the range of magnetic fields calculated. The metastable states found for small enough fields terminate at a rather well-defined "coercive field," where no singular behavior of the susceptibility can be detected, within the accuracy of the numerical calculation. In order to explain these results an approximate theory of cluster dynamics is derived from the master equation, and Fisher's static-cluster model, generalizing the more conventional nucleation theories. It is shown that the properties of the metastable states (including their lifetimes) derived from this treatment are quite consistent with the numerical data, although the details of the dynamics of cluster distributions are somewhat different. This treatment contradicts the mean-field theory and other extrapolations, predicting the existence of a spinodal curve. In order to elucidate the possible analytic behavior of the coercive field we discuss a generalization of the scaling equation of state, which includes the metastable states in agreement with our data.