Cell-dynamical simulation of magnetic hysteresis in the two-dimensional Ising system

Abstract

We present results from numerical simulations using a ``cell-dynamical system'' to obtain solutions to the time-dependent Ginzburg-Landau equation for a scalar, two-dimensional (2D), (${\mathrm{\ensuremath{\Phi}}}^{2}$${)}^{2}$ model in the presence of a sinusoidal external magnetic field. Our results confirm a recent scaling law proposed by Rao, Krishnamurthy, and Pandit [Phys. Rev. B 42, 856 (1990)], and are also in excellent agreement with recent Monte Carlo simulations of hysteretic behavior of 2D Ising spins by Lo and Pelcovits [Phys. Rev. A 42, 7471 (1990)].