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)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)L(t)θP(t)\sim L(t)^{-\theta'}, where θ=0.420±0.009\theta' = 0.420\pm 0.009. The value of θ\theta' 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)(lnt)θdP(t)\sim (\ln t)^{-\theta_d}, where θd=0.63±0.01\theta_d = 0.63\pm 0.01.Comment: references updated, very minor amendment to abstract and the labelling of figures. To be published in Phys Rev E (Rapid Communications), 1 March 199

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