Disorder-induced critical phenomena in hysteresis: Numerical scaling in three and higher dimensions

We present numerical simulations of avalanches and critical phenomena assoc iated with hysteresis loops, modeled using the zero-temperature random-fiel d: Ising model. We study the transition between smooth hysteresis loops and loops with a sharp jump in the magnetization, as the disorder in our model is decreased. In a large region near the critical paint, we find scaling a nd critical phenomena, which are well described by the results of an is an element of expansion about six dimensions. We present the results of simula tions in three, four, and five dimensions, with systems with up to a billio n spins(1000(3)). [S0163- 1829(99)03709-1].