HYSTERESIS, AVALANCHES, AND DISORDER-INDUCED CRITICAL SCALING - A RENORMALIZATION-GROUP APPROACH

Hysteresis loops are often seen in experiments at first-order phase tr ansformations, when the system goes out of equilibrium. They may have a macroscopic jump (roughly as in the supercooling of liquids) or they may be smoothly varying (as seen in most magnets). We have studied th e nonequilibrium zero-temperature random-field Ising-model as a model for hysteretic behavior at first-order phase transformations. As disor der is added, one finds a transition where the jump in the magnetizati on (corresponding to an infinite avalanche) decreases to zero. At this transition we find a diverging length scale, power-law distributions of noise (avalanches), and universal behavior. We expand the critical exponents about mean-field theory in 6-epsilon dimensions. Using a map ping to the pure Ising model, we Borel sum the 6-epsilon expansion to O(epsilon(5)) for the correlation length exponent. We have developed a method for directly calculating avalanche distribution exponents, whi ch we perform to O(epsilon). Our analytical predictions agree with num erical exponents in two, three, four, and five dimensions [Perkovic et al., Phys. Rev. Lett. 75, 4528 (1995)].