STOCHASTIC HYSTERESIS AND RESONANCE IN A KINETIC ISING SYSTEM

We study hysteresis for a two-dimensional, spin-1/2, nearest-neighbor, kinetic Ising ferromagnet in an oscillating field, using Monte Carlo simulations and analytical theory. Attention is focused on small syste ms and weak field amplitudes at a temperature below T-c. For these res tricted parameters, the magnetization switches through random nucleati on of a single droplet of spins aligned with the applied field. We ana lyze the stochastic hysteresis observed in this parameter regime, usin g time-dependent nucleation theory and the theory of variable-rate Mar kov processes. The theory enables us to accurately predict the results of extensive Monte Carlo simulations, without the use of any adjustab le parameters. The stochastic response is qualitatively different from what is observed, either in mean-field models or in simulations of la rger spatially extended systems. We consider the frequency dependence of the probability density for the hysteresis-loop area and show that its average slowly crosses over to a logarithmic decay with frequency and amplitude for asymptotically low frequencies. Both the average loo p area and the residence-time distributions for the magnetization show evidence of stochastic resonance. We also demonstrate a connection be tween the residence-time distributions and the power spectral densitie s of the magnetization time series. In addition to their significance for the interpretation of recent experiments in condensed-matter physi cs, including studies of switching in ferromagnetic and ferroelectric nanoparticles and ultrathin films, our results are relevant to the gen eral theory of periodically driven arrays of coupled, bistable systems with stochastic noise.