Hysteresis and avalanches in the random anisotropy Ising model

Abstract

The behavior of the random anisotropy Ising model at $T=0$ under local relaxation dynamics is studied. The model includes a dominant short-range ferromagnetic interaction and assumes an infinite anisotropy at each site along local anisotropy axes which are randomly aligned. As a consequence, some of the effective interactions become antiferromagneticlike and frustration appears. Two different random distributions of anisotropy axes have been studied. Both are characterized by a parameter that allows control of the degree of disorder in the system. By using numerical simulations we analyze the hysteresis loop properties and characterize the statistical distribution of avalanches occurring during the metastable evolution of the system driven by an external field. A disorder-induced critical point is found in which the hysteresis loop changes from displaying a typical ferromagnetic magnetization jump (large avalanche spanning a macroscopic fraction of the system) to a rather smooth loop exhibiting only tiny avalanches. The critical point is characterized by a set of critical exponents, which are consistent with the universal values proposed from the study of other simpler models.