Breakdown of self-similar scaling in the two-dimensional random-field Ising model: A Monte Carlo study

We have simulated the two-dimensional ferromagnetic Ising model in a random magnetic field with spin-flip dynamics. After the system is deeply quenched into the unstable region of the phase diagram, we observe novel dynamical behavior, during an early-to-intermediate time regime, for the average size of the growing domains, R¯. We find that self-similar scaling for the structure factor [that is, scaling to a single time-dependent length such as R¯(t)] breaks down for long times. Our results may have relevance to the problem of island-growth kinetics in some chemisorbed systems.