Scaling of hysteresis in the Ising model and cell-dynamical systems in a linearly varying external field.

Abstract

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\ifmmode \dot{}\else \.{}\fi{} as A=${\mathit{A}}_{0}$+aH${\mathrm{\ifmmode \dot{}\else \.{}\fi{}}}^{\mathrm{\ensuremath{\alpha}}}$, with a nearly constant \ensuremath{\alpha}\ensuremath{\sim}0.36\ifmmode\pm\else\textpm\fi{}0.08 for the Ising model and 0.66\ifmmode\pm\else\textpm\fi{}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 ${\mathit{A}}_{0}$=0 and an \ensuremath{\alpha} that increases with temperature and disorder.