Conserved dynamics of a two-dimensional random-field model

We present results from a numerical study of the growth of domains in two dimensions, following a low-temperature quench, in a time-dependent Ginzburg-Landau model in the presence of a quenched random field. The order parameter is conserved during the temporal evolution of the system. We find that, at late times, the domains grow logarithmically in time, consistent with studies done for a nonconserved order parameter. We present clear evidence for a breakdown of dynamical scaling of the structure factor. We also demonstrate a crossover behavior exhibited by the tail of the structure factor---the standard Porod-like behavior changes over to a ''polymerlike'' behavior as the strength of the randomness is increased