Exact results for mean-field zero-temperature random-field Ising model

Abstract

We present an analysis of the dynamical critical behavior of the mean-field zero-temperature random-field Ising model, based on the probability of finding a given sequence in the response signal, which has the form of a Markov chain with Poisson transition probabilities. We provide an exact description of the avalanche duration distribution, the absolute probabilities of signal values, and the signal time-autocorrelation function. The overall behavior of these quantities depends on their characteristic lengths, which all diverge near the critical point (z = 1) as ∼ 1/| ln(z)|, where z is a control parameter of the underlying dynamics. Our findings are corroborated with the results of extensive simulations. © EDP Sciences.