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{\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)].

• Received 11 March 1991

DOI:https://doi.org/10.1103/PhysRevB.45.7828