Persistence in the Zero-Temperature Dynamics of the Disordered Ising Model

The non-equilibrium dynamics of the strongly disordered random-bond Ising model in two-dimensions (2d) is investigated numerically. The persistence probability, P(t), of spins which do not flip by time t is found to decay to a non-zero, disorder dependent, value $P(\infty)$. We find that $p(t)=P(t)-P(\infty)$ decays exponentially to zero at large times. Furthermore, the fraction of spins which never flip is a monotonically increasing function over the range of bond-disorder considered. Our findings, which are consistent with a recent result of Newman and Stein, suggest that persistence in disordered and pure systems falls into different classes. Furthermore, its behaviour would also appear to depend crucially on the strength of the disorder present.