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We present comprehensive numerical results for domain growth in thetwo-dimensional {\it Random Bond Ising Model} (RBIM) with nonconserved Glauberkinetics. We characterize the evolution via the {\it domain growth law}, andtwo-time quantities like the {\it autocorrelation function} and {\itautoresponse function}. Our results clearly establish that the growth law showsa crossover from a pre-asymptotic regime with "power-law growth with adisorder-dependent exponent" to an asymptotic regime with "logarithmic growth".We compare this behavior with previous results on one-dimensional disorderedsystems and we propose a unifying picture in a renormalization group framework.We also study the corresponding crossover in the scaling functions for thetwo-time quantities. Super-universality is found not to hold. Clear evidencesupporting the dimensionality dependence of the scaling exponent of theautoresponse function is obtained.

Growth Law and Superuniversality in the Coarsening of Disordered Ferromagnets