Mechanism for the failure of the Edwards hypothesis in the SK spin glass

Eastham, P. R.; Blythe, R. A.; Bray, A. J.; Moore, M . A.

Mechanism for the failure of the Edwards hypothesis in the SK spin glass

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Description

The dynamics of the SK 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, $p(λ)$, is small at $λ=0$. 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 modelling 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.
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