The effect of finite driving rate on avalanche distributions

Abstract

We study distributions of spin avalanches in the three-dimensional nonequilibrium zero temperature random field Ising model driven by external magnetic field that is increased at constant rate. Our results show that avalanche distributions are affected by the driving regime and although the avalanche properties (e.g. size) remain power-law distributed above critical disorder, the scaling exponents vary with the driving rate. For slow driving, the integral distributions of nonspanning avalanches are almost the same as in the adiabatic and quasi-static driving regime and therefore described by constant values of power-law exponents. Owing to temporal overlapping and merging of avalanches, these distributions become markedly different with the increased driving rate which causes an increase of exponent values in the range of moderate driving rates and their saturation for fast driving. The integral distributions of all avalanches behave similarly but without the saturation of exponents for fast driving. Our results, based on extensive numerical simulations, could be relevant for studies of variety of systems in finite driving regime, particularly those with experimental realizations that are not easily attainable.