HYSTERESIS AND HIERARCHIES - DYNAMICS OF DISORDER-DRIVEN 1ST-ORDER PHASE-TRANSFORMATIONS

We use the zero-temperature random-field Ising model to study hysteret ic behavior at first-order phase transitions. Sweeping the external fi eld through zero, the model exhibits hysteresis, the return-point memo ry effect, and avalanche fluctuations. There is a critical value of di sorder at which a jump in the magnetization (corresponding to an infin ite avalanche) first occurs. We study the universal behavior at this c ritical point using mean-field theory, and also present results of num erical simulations in three dimensions.