Scaling domains in the nonequilibrium athermal random field Ising model of finite systems

Abstract

We analyze the nonequilibrium athermal random field Ising model (RFIM) at equilateral cubic lattices of finite size L and show that the entire range of disorder consists of three distinct domains in which the model manifests different scaling behaviour. The first domain contains the values of disorder R that are below the critical disorder Rc where the spanning avalanches almost surely appear when the system is driven by the external magnetic field. The spanning avalanches become unlikely for disorders above the size-dependent effective disorder Rceff(L) > Rc, and the system response is size-independent. Between the foregoing two lies the domain of transitional disorders Rc < R < Rceff(L) vanishing in the thermodynamic limit. In this domain, not recognized in the literature so far, all types of spanning avalanches exist, whereas for R < Rc only the avalanches spanning all three dimensions are present. Like for R < Rc the data collapsing is possible only for distributions having the same value of (1 - Rc/R)L1/ν, however with different universal scaling functions than in R < Rc case; ν is the correlation length exponent. The foregoing findings follow from the extensive simulations of L ≼ 2048 systems enabling us to propose modified values of some of the RFIM critical exponents and nonuniversal critical parameters as well as the analytic forms of universal scaling functions and different definitions of reduced magnetization and reduced magnetic field.