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# Stochastic Hysteresis and Resonance in a Kinetic Ising System

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### Abstract

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 systems and weak field amplitudes at a temperature below $$T_{c}$$. For these restricted parameters, the magnetization switches through random nucleation of a single droplet of spins aligned with the applied field. We analyze the stochastic hysteresis observed in this parameter regime, using time-dependent nucleation theory and the theory of variable-rate Markov processes. The theory enables us to accurately predict the results of extensive Monte Carlo simulations, without the use of any adjustable parameters. The stochastic response is qualitatively different from what is observed, either in mean-field models or in simulations of larger 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 loop area and the residence-time distributions for the magnetization show evidence of stochastic resonance. We also demonstrate a connection between the residence-time distributions and the power spectral densities of the magnetization time series. In addition to their significance for the interpretation of recent experiments in condensed-matter physics, including studies of switching in ferromagnetic and ferroelectric nanoparticles and ultrathin films, our results are relevant to the general theory of periodically driven arrays of coupled, bistable systems with stochastic noise.

### Most cited references80

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### Stochastic resonance

(1998)
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### Time‐Dependent Statistics of the Ising Model

(1963)
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### A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening

(1979)
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### Author and article information

###### Journal
02 December 1997
1998-02-25
###### Article
10.1103/PhysRevE.57.6512
cond-mat/9712021
Phys. Rev. E 57 6512-6533 (1998)
35 pages. Submitted to Phys. Rev. E Minor revisions to the text and updated references
cond-mat.mtrl-sci chao-dyn cond-mat.stat-mech nlin.CD

Condensed matter, Nonlinear & Complex systems