Persistence and the Random Bond Ising Model in Two Dimensions

We study the zero-temperature persistence phenomenon in the random bond $\pm J$ Ising model on a square lattice via extensive numerical simulations. We find strong evidence for blocking\rq regardless of the amount disorder present in the system. The fraction of spins which {\it never} flips displays interesting non-monotonic, double-humped behaviour as the concentration of ferromagnetic bonds $p$ is varied from zero to one. The peak is identified with the onset of the zero-temperature spin glass transition in the model. The residual persistence is found to decay algebraically and the persistence exponent $\theta (p)\approx 0.9$ over the range $0.1\le p\le 0.9$. Our results are completely consistent with the result of Gandolfi, Newman and Stein for infinite systems that this model has mixed\rq behaviour, namely positive fractions of spins that flip finitely and infinitely often, respectively. [Gandolfi, Newman and Stein, Commun. Math. Phys. {\bf 214} 373, (2000).]