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

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

2006-01-18

arxiv.org/abs/cond-mat/0601402v2

Phys. Rev. B 74, 020406(R) (2006)

Physics

Condensed Matter

Disordered Systems and Neural Networks

5 pages, new title, modified text, additional references

Scientific paper

10.1103/PhysRevB.74.020406

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, $p(\lambda)$, is small at $\lambda=0$. 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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