Disorder-driven first-order phase transformations: A model for hysteresis

Abstract

Hysteresis loops in some magnetic systems are composed of small avalanches (manifesting themselves as Barkhausen pulses). Hysteresis loops in other first-order phase transitions (including some magnetic systems) often occur via one large avalanche. The transition between these two limiting cases is studied, by varying the disorder in the zero-temperature random-field Ising model. Sweeping the external field through zero at weak disorder, we get one large avalanche with small precursors and aftershocks. At strong disorder, we get a distribution of small avalanches (small Barkhausen effect). At the critical value of disorder where a macroscopic jump in the magnetization first occurs, universal power-law behavior of the magnetization and of the distribution of (Barkhausen) avalanches is found. This transition is studied by mean-field theory, perturbative expansions, and numerical simulation in three dimensions.