Hysteresis and avalanches in the random anisotropy Ising model

Abstract

The behavior of the random anisotropy Ising model at Tϭ0 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 system͒ 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.

Phase Transitions in a Disordered System in and out of Equilibrium

“…Numerical simulations and analytical results have shown that a disorder-induced transition in the hysteresis loop can be observed in the random bond Ising model [30], in the random-field O(N) model [31], in the random anisotropy model [32], and in the random Blume-Emery-Griffith model [30]. All these systems also show a transition in equilibrium and it would be interesting to compare their DS and GS.…”

Nonergodic thermodynamics of disordered ferromagnets and ferroelectrics

“…The smaller loops inside the main one and evolution via macroscopic spin avalanches on the main loop are shown to exist in Edwards-Anderson 10 and Sherrington-Kirkpatrick 11,12 spin-glass models. The existence of hysteresis loops is established in random -anisotropy model 13 . The new hard-spin mean-field method is developed for frustrated random -bond systems 14,15,16 which provides the evidences for the existence of multiple metastable states and can describe a number of nonergodic phenomena with less simulation efforts.…”

Effect of randomness on ferroelastic transitions: Disorder-induced hysteresis loop rounding in Ti-Nb-O martensitic alloy

“…2,[16][17][18][19][20][21][22][23][24] A main difference among them is the number of the degrees of freedom; each spin variable s i has two states ͑s i =+1,−1͒ in Ising-type model, 2,[16][17][18][19][20][21][22] three states ͑s i =+1,0,−1͒ in Blume-Emery-Griffith-type model, 23 and an arbitrary number of states in Potts-type model, 24 respectively. Thus, when the system transforms into energetically equivalent states, like a martensitic system which has several degenerate domains ͑or variants͒, RF Potts model ͑RFPM͒ ͑Ref.…”