Hysteresis loops are often seen in experiments at first order phase transformations, 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 the nonequilibrium zerotemperature random-field Ising-model as a model for hysteretic behavior at first order phase transformations. As disorder is added, one finds a transition where the jump in the magnetization (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 − ǫ dimensions. Using a mapping to the pure Ising model, we Borel sum the 6−ǫ expansion to O(ǫ5) for the correlation length exponent. We have developed a new method for directly calculating avalanche distribution exponents, which we perform to O(ǫ). Numerical exponents in three, four, and five dimensions are in good agreement with the analytical predictions. Some suggestions for further analyses and 1 experiments are also discussed
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