Growth law and superuniversality in the coarsening of disordered ferromagnets

We present comprehensive numerical results for domain growth in the two-dimensional random bond Ising model (RBIM) with non-conserved Glauber kinetics. We characterize the evolution via the domain growth law, and two-time quantities like the autocorrelation function and autoresponse function. Our results show evidence for the crossover from a pre-asymptotic regime with 'power-law growth with a disorder-dependent exponent' to an asymptotic regime with 'logarithmic growth'. We compare this behavior with previous results on one-dimensional disordered systems and we propose a unifying picture in a renormalization group framework. We also study the corresponding crossover in the scaling functions for the two-time quantities. Superuniversality is found not to hold. Clear evidence supporting the dimensionality dependence of the scaling exponent of the autoresponse function is obtained.