Avalanches, Barkhausen noise, and disorder-induced critical behavior

Abstract

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 seen in the supercooling of liquids, or they may be smoothly varying, as seen in most magnets. We have studied the nonequilibrium zero-temperature 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 the model exhibits power law distributions of noise (avalanches), universal behavior, and a diverging length scale, which should be detectable in acoustic emission and other noise measurements. We study universal properties of this critical point using renormalization group methods and numerical simulations. Connections to experimental systems such as athermal martensitic phase transitions (with and without ‘‘bursts’’) and the Barkhausen effect in magnetic systems will be discussed. Similar ideas can also be applied to the interpretation of the Gutenberg–Richter scaling law in the statistics of earthquakes.