Blocking and Persistence in the Disordered Ising Model

Abstract

The nonequilibrium dynamics of the disordered (bond-diluted and the ± J) Ising model in two-dimensions (2d) is investigated numerically. In both cases we find evidence for “blocking”. The bond-diluted case is studied for the complete 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 ≤ 0.6) we find that the residual persistence r(t) = P(t) - P(∞) decays exponentially to zero at large times. For the ±J model the residual persistence decays algebraically, just as in the pure model, but with a different persistence exponent. Our results for strong dilution are consistent with recent work of Newman and Stein. The present study suggests that persistence in disordered and pure systems falls into different classes. Furthermore, its behaviour would also appear to depend crucially on the type of disorder present.