Persistence and the random bond Ising model in two dimensions

S. Jain*, H. Flynn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We study the zero-temperature persistence phenomenon in the random bond ±J Ising model on a square lattice via extensive numerical simulations. We find strong evidence for "blocking" regardless of the amount disorder present in the system. The fraction of spins which never flips displays interesting nonmonotonic, double-humped behavior 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 θ (p) 0.9 over the range 0.1≤p≤0.9. Our results are completely consistent with the result of Gandolfi, Newman, and Stein for infinite systems that this model has "mixed" behavior, namely positive fractions of spins that flip finitely and infinitely often, respectively. [Gandolfi, Newman and Stein, Commun. Math. Phys. 214, 373 (2000).]

Original languageEnglish
Article number025701
JournalPhysical Review E
Issue number2
Publication statusPublished - 3 Feb 2006

Bibliographical note

©2006 American Physical Society. Persistence and the random bond Ising model in two dimensions
S. Jain and H. Flynn
Phys. Rev. E 73, 025701(R) – Published 3 February 2006


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