Experiments on ferromagnetic thin films have measured the dependence of the
hysteresis loop area on the amplitude and frequency of the external field,
A=A(H0β,Ο), and approximate agreement with numerical simulations of
Ising models has been reported. Here we present numerical and theoretical
calculations of A in the low-frequency regime for two values of H0β,
which bracket a temperature and system-size dependent crossover field. Our
previous Monte Carlo studies have shown that the hysteretic response of the
kinetic Ising model is qualitatively different for amplitudes above and below
this crossover field. Using droplet theory, we derive analytic expressions for
the low-frequency asymptotic behavior of the hysteresis loop area. In both
field regimes, the loop area exhibits an extremely slow approach to an
asymptotic, logarithmic frequency dependence of the form Aββ[ln(H0βΟ)]β1. Our results are relevant to the interpretation of data
from experiments and simulations, on the basis of which power-law exponents for
the hysteresis-loop area have been reported.Comment: 9 pages including 3 figures. Submitted as a manuscript for the 7th
Joint MMM-Intermag conference. To be published in the Journal of Applied
Physics and the IEEE Transactions on Magnetics. Contains 1 updated figure and
revised tex