Monte Carlo study of the equilibration of the random-field Ising model

Monte Carlo simulations are used to study the equilibration of Ising systems in random magnetic fields at low temperatures (T) following a quench from high T in two dimensions. The rate at which domains grow with time is determined as a function of the random-field strength H, the linear dimension of the system L, and temperature T. Domains are found to grow logarithmically with time. For small systems L$L^{\mathrm{*}}$=(4J/H${)}^2$, the exponents a and b of the exponential equilibration time τ∼exp[(H/T${)}^a$ $L^b$] are found to be a≃1.0, b≃0.5 in agreement with recent calculations based on approximate interface models. We tested the L and H/T dependence of τ in three dimensions for L$L^{\mathrm{*}}$ and found a≃1.0 and b≃0.5 also in three dimensions.