SCALING OF HYSTERESIS IN THE ISING-MODEL AND CELL-DYNAMICAL SYSTEMS IN A LINEARLY VARYING EXTERNAL-FIELD

We present results from simulations of the hysteresis loops in the two-dimensional (2D) Ising model and a cell-dynamical system (CDS) in a linearly, rather than sinusoidally, varying external field. We find in the CDS a disorder-induced transition, which has behavior similar to the critical point in the 2D Ising model. Below the critical point, the area of the hysteresis loops, representing the dissipation per cycle; scales with the rate of the driving field H as A = A(o) + alpha H-alpha, with a nearly constant alpha similar to 0.36 +/- 0.08 for the Ising model and 0.66 +/- 0.02 for the CDS. Thus, the CDS belongs to the class of mean-field models, which is different from that of the Ising model. Above the critical point, both the Ising model and the CDS give A(o) = 0 and an a that increases with temperature and disorder.