Zero Temperature Dynamics of the Weakly Disordered Ising Model

The Glauber dynamics of the pure and weakly disordered random-bond 2d Ising model is studied at zero-temperature. A single characteristic length scale, $L(t)$, is extracted from the equal time correlation function. In the pure case, the persistence probability decreases algebraically with the coarsening length scale. In the disordered case, three distinct regimes are identified: a short time regime where the behaviour is pure-like; an intermediate regime where the persistence probability decays non-algebraically 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 $P(t)\sim L(t{)}^{-{\theta }^{\mathrm{\prime }}}$, where ${\theta }^{\mathrm{\prime }}=0.420\pm 0.009$. The value of ${\theta }^{\mathrm{\prime }}$ 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, $P(t)\sim (\ln t{)}^{-{\theta }_d}$, where $\theta_d = 0.63\pm 0.01$.