Short-range spin glasses and Random Overlap Structures

Abstract

Properties of Random Overlap Structures (ROSt)'s constructed from the Edwards-Anderson (EA) Spin Glass model on ${\mathbb{Z}}^d$ with periodic boundary conditions are studied. ROSt's are $\mathbb{N}\times \mathbb{N}$ random matrices whose entries are the overlaps of spin configurations sampled from the Gibbs measure. Since the ROSt construction is the same for mean-field models (like the Sherrington-Kirkpatrick model) as for short-range ones (like the EA model), the setup is a good common ground to study the effect of dimensionality on the properties of the Gibbs measure. In this spirit, it is shown, using translation invariance, that the ROSt of the EA model possesses a local stability that is stronger than stochastic stability, a property known to hold at almost all temperatures in many spin glass models with Gaussian couplings. This fact is used to prove stochastic stability for the EA spin glass at all temperatures and for a wide range of coupling distributions. On the way, a theorem of Newman and Stein about the pure state decomposition of the EA model is recovered and extended.

27 pages

References in corpus (4)

• Spin glass models from the point of view of spin distributions
• Stochastic Stability: a Review and Some Perspectives
• Interaction-Flip Identities in Spin Glasses
• On the Dovbysh-Sudakov representation result

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• Stationarization and Multithermalization in spin glasses
• A Relation between Disorder Chaos and Incongruent States in Spin Glasses on ${\mathbb{Z}}^d$
• Zero-Temperature Fluctuations in Short-Range Spin Glasses