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      Kinetic Ising model in an oscillating field: Avrami theory for the hysteretic response and finite-size scaling for the dynamic phase transition

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          Abstract

          Hysteresis is studied 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 large systems and strong field amplitudes at a temperature below T_c. In this parameter regime, the magnetization switches through random nucleation and subsequent growth of many droplets of spins aligned with the applied field. Using a time-dependent extension of the Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory of metastable decay, we analyze the statistical properties of the hysteresis-loop area and the correlation between the magnetization and the applied field. This analysis enables us to accurately predict the results of extensive Monte Carlo simulations. The average loop area exhibits an extremely slow approach to an asymptotic, logarithmic dependence on the product of the amplitude and the frequency of the applied field. This may explain the inconsistent exponent estimates reported in previous attempts to fit experimental and numerical data for the low-frequency behavior of this quantity to a power law. At higher frequencies we observe a dynamic phase transition. Applying standard finite-size scaling techniques from the theory of second-order equilibrium phase transitions to this nonequilibrium phase transition, we obtain estimates for the transition frequency and the critical exponents (beta/nu \approx 0.11, gamma/nu \approx 1.84 and nu \approx 1.1). In addition to their significance for the interpretation of recent experiments on switching in ferromagnetic and ferroelectric nanoparticles and thin films, our results provide evidence for the relevance of universality and finite-size scaling to dynamic phase transitions in spatially extended nonstationary systems.

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          Most cited references 94

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          Stochastic resonance

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            Kinetics of Phase Change. I General Theory

             Melvin Avrami (1939)
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              Time‐Dependent Statistics of the Ising Model

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                Author and article information

                Journal
                08 September 1998
                1998-12-15
                Article
                10.1103/PhysRevE.59.2710
                cond-mat/9809136
                Custom metadata
                FSU-SCRI-98-83
                Phys. Rev. E 59, 2710-2729 (1999).
                24 pages RevTex with postscript figures. Minor revisions. In press in PRE
                cond-mat.stat-mech chao-dyn cond-mat.mtrl-sci nlin.CD

                Condensed matter, Nonlinear & Complex systems

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