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

We present numerical simulations of avalanches and critical phenomena associated with hysteresis loops, modeled using the zero-temperature random-field 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 point, we find scaling and critical phenomena, which are well described by the results of an $\epsilon$ expansion about six dimensions. We present the results of simulations in three, four, and five dimensions, with systems with up to a billion spins ${(1000\mathrm{}}^3).\mathrm{}$