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

Hysteresis is studied for a two-dimensional, spin-1/2, nearest-neighbor. ki netic Ising ferromagnet in a sinusoidally oscillating field, using Monte Ca rlo simulations and analytical theory. Attention is focused on large system s and moderately strong field amplitudes at a temperature below T-c. In thi s parameter regime, the magnetization switches through random nucleation an d subsequent growth of many droplets of spins aligned with the applied fiel d. Using a time-dependent extension of the Kolmogorov-Johnson-Mehl-Avrami t heory of metastable decay, we analyze the statistical properties of the hys teresis-loop area and the correlation between the magnetization and the hel d. This analysis enables us to accurately predict the results of extensive Monte Carlo simulations. The average loop area exhibits an extremely slow a pproach to an asymptotic, logarithmic dependence on the product of the ampl itude and the field frequency. This may explain the inconsistent exponent e stimates reported in previous attempts to fit experimental and numerical da ta for the low-frequency behavior of this quantity to a power law. At highe r frequencies we observe a dynamic phase transition. Applying standard fini te-size scaling techniques from the theory of second-order equilibrium phas e transitions to this nonequilibrium transition, we obtain estimates for th e transition frequency;nd the critical exponents (beta/nu approximate to 0. 11, gamma/nu approximate to 1.84, and nu approximate to 1.1). In addition t o their significance for the interpretation of recent experiments on switch ing in ferromagnetic and ferroelectric nanoparticles and thin films, our re sults provide evidence for the relevance of universality and finite-size sc aling to dynamic phase transitions in spatially extended nonstationary syst ems. [S1063-651X(99)08303-8].