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

Abstract

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.

arXiv comment5 pages, new title, modified text, additional references

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• Local field distributions in spin glasses
• Devising a protocol-related statistical mechanics framework for granular materials
• Mean-field description of plastic flow in amorphous solids
• Ground States of the Sherrington-Kirkpatrick Spin Glass with Levy Bonds
• Self-organized critical behavior and marginality in Ising spin glasses
• Coordination problems on networks revisited: statics and dynamics
• Hysteretic response to different modes of ramping an external field in sparse and dense Ising spin glasses