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*=(4J/H)2, the exponents a and b of the exponential equilibration time exp[(H/T)aLb] are found to be a 1.0, b0.5 in agreement with recent calculations based on approximate interface models. We tested the L and H/T dependence of in three dimensions for L<L* and found a 1.0 and b 0.5 also in three dimensions. © 1985 The American Physical Society.