Zero-temperature dynamics of the weakly disordered Ising model

The Glauber dynamics of the pure and weakly disordered random-bond two-dimensional (2D) Ising model is studied at zero temperature. A single characteristic length scale, $L\left(t\right),$ is extracted from the equal time correlation function. In the pure case, the persistence probability, $P\left(t\right),$ decreases algebraically with the coarsening length scale. In the disordered case, three distinct regimes are identified: a short time regime where the behavior is purelike; an intermediate regime where the persistence probability decays nonalgebraically with time; and a long time regime where the domains freeze and there is a cessation of growth. In the intermediate regime, we find that $P\left(t\right)\mathrm{}\sim {L\left(t\right)\mathrm{}}^{-{\theta }^{\prime }},$ where ${\theta }^{\prime }=0.420\mathrm{}\pm \mathrm{0.009.}$ The value of ${\theta }^{\prime }$ is consistent with that found for the pure 2D Ising model at zero temperature. Our results in the intermediate regime are consistent with a logarithmic decay of the persistence probability with time, $P\left(t\right)\mathrm{}\sim (\ln {t)}^{-{\theta }_d},$ where ${\theta }_d=0.63\mathrm{}\pm \mathrm{0.01.}$