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Mechanism for the failure of the Edwards hypothesis in the Sherrington-Kirkpatrick spin glass
EASTHAM, PAUL
The dynamics of the Sherrington-Kirkpatrick model at T=0 starting from random spin configurations is considered. The metastable states reached by such dynamics are atypical of such states as a whole, in that the probability density of site energies, p , is small at =0. Since virtually all metastable states have a much larger p 0 , this behavior demonstrates a qualitative failure of the Edwards hypothesis. We look for its origins by modeling the changes in the site energies during the dynamics as a Markov process. We show how the small p(0) arises from features of the Markov process that have a clear physical basis in the spin glass, and hence explain the failure of the Edwards hypothesis.
Keyword(s): Atomic, molecular and chemical physics; spin glass; Sherrington-Kirkpatrick; Edwards hypothesis
Publication Date:
2006
Type: Journal article
Peer-Reviewed: Yes
Language(s): English
Institution: Trinity College Dublin
Citation(s): Eastham, PR, Blythe, RA, Bray, AJ, Moore, MA, Mechanism for the failure of the Edwards hypothesis in the Sherrington-Kirkpatrick spin glass, Physical Review B, 74, 2006, 020406
First Indexed: 2014-05-13 05:12:12 Last Updated: 2017-04-14 05:13:20