Crossover from three-dimensional to two-dimensional systems in the nonequilibrium zero-temperature random-field Ising model

Abstract

We present extensive numerical studies of the crossover from three-dimensional to two-dimensional systems in the nonequilibrium zero-temperature random-field Ising model with metastable dynamics. Bivariate finite-size scaling hypotheses are presented for systems with sizes L °ø L °ø l which explain the size-driven critical crossover from two dimensions (l = const, L→∞) to three dimensions (l ∝ L→∞). A model of effective critical disorder Reffc (l,L) with a unique fitting parameter and no free parameters in the Reffc (l,L→∞) limit is proposed, together with expressions for the scaling of avalanche distributions bringing important implications for related experimental data analysis, especially in the case of thin three-dimensional systems.