Nucleation and hysteresis in Ising model: Classical theory versus computer simulation

TL;DR

This study investigates nucleation and hysteresis in the Ising model across multiple dimensions using Monte Carlo simulations, confirming classical theory predictions and exploring dynamic responses under oscillating fields.

Contribution

It provides a comprehensive numerical analysis of nucleation times, crossover behaviors, and hysteresis in the Ising model, validating classical nucleation theory through extensive simulations.

Findings

Nucleation time scales as a power of magnetic field in all dimensions.

Crossover from coalescence to nucleation observed in all dimensions.

Hysteresis behavior aligns with classical theoretical predictions.

Abstract

We have studied the nucleation in the nearest neighbour ferromagnetic Ising model, in different (d) dimensions, by extensive Monte Carlo simulation using the heat-bath dynamics. The nucleation time (tau) has been studied as a function of the magnetic field (h) for various system sizes in different dimensions (d=2,3,4). The logarithm of the nucleation time is found to be proportional to the power (-(d-1)) of the magnetic field (h) in d dimensions. The size dependent crossover from coalescence to nucleation regime is observed in all dimensions. The distribution of metastable lifetimes are studied in both regions. The numerical results are compared and found to be consistent with the classical theoretical predictions. In two dimensions, we have also studied the dynamical response to a sinusoidally oscillating magnetic field. The reversal time is studied as a function of the inverse of the coercive field. The applicability of the classical nucleation theory to study the hysteresis and coercivity has been discussed.