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 3, 4, and 5 dimensions, with systems with up to a billion spins (1000^3). 
Olga Perkovic, Karin A. Dahmen, and James P. Sethna