Persistence and the Random Bond Ising Model in Two Dimensions
arXiv:cond-mat/0512663 · doi:10.1103/PhysRevE.73.025701
Abstract
We study the zero-temperature persistence phenomenon in the random bond 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 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 over the range . 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).]
9 pages, 5 figures
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