Non-Equilibrium Dynamics of the Disordered Ising Model

Abstract

The non-equilibrium dynamics of the bond-diluted Ising model in two-dimensions (2d) is investigated numerically for a range of bond concentration 0 ≤ p ≤ 1. The fraction of spins which never flip, P (∞), is found to increase monotonically from zero for p = 0 with increasing bond concentration to a maximum value of about 0.46 for p = 0.5 and then decreases to zero for p = 1. For strong bond-dilution (0 ≤ p ≤ 0.5) we find that r(t) = P (t)−P (∞) decays exponentially to zero at large times. For weak dilution (0.975 ≤ p < 1.0), three distinct regimes are identified: a short time regime where the behaviour is purelike; an intermediate regime where the persistence probability decays nonalgebraically with time; and a long time ‘frozen’ regime where the domains cease to grow. Our results for strong dilution are consistent with recent work of Newman and Stein, and suggest that persistence in diluted and pure systems falls into different classes. Furthermore, its behaviour would also appear to depend crucially on the strength of the dilution present.