Domain growth in the random-field Ising model: The breakdown of self-similar scaling in two dimensions

We study a continuum random-field model of unstable domain growth in deep far-from-equilibrium quenches. We analyze the interfacial dynamics of the evolving domains and determine the growth laws and the structure factors in two and three dimensions. Our results can be interpreted as kinetic arguments, complementary to the equilibrium arguments of Imry and Ma, which are consistent with a lower critical dimension $d_l=2\mathrm{}$. In $d=2\mathrm{}$ dimensions, we find that phase separation apparently stops, and that, as time tends to infinity, the renormalized "surface tension" vanishes. The results we obtain for the structure factor indicate that nonequilibrium scaling breaks down for $d\le 2$. Our theoretical predictions can be tested experimentally, or by computer simulation.