Hysteresis and hierarchies: dynamics of disorder-driven first-order   phase transformations
  We use the zero-temperature random-field Ising model to study hysteretic behavior at first-order phase transitions. Sweeping the external field through zero, the model exhibits hysteresis, the return-point memory effect, and avalanche fluctuations. There is a critical value of disorder at which a jump in the magnetization (corresponding to an infinite avalanche) first occurs. We study the universal behavior at this critical point using mean-field theory, and also present preliminary results of numerical simulations in three dimensions. 
James P. Sethna, Karin Dahmen, Sivan Kartha, James A. Krumhansl, Bruce   W. Roberts, and Joel D. Shore