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Short-Range Spin Glasses and Random Overlap Structures

Short-Range Spin Glasses and Random Overlap Structures Properties of Random Overlap Structures (ROSt)’s constructed from the Edwards-Anderson (EA) Spin Glass model on ℤ d with periodic boundary conditions are studied. ROSt’s are ℕ×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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Statistical Physics Springer Journals

Short-Range Spin Glasses and Random Overlap Structures

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References (32)

Publisher
Springer Journals
Copyright
Copyright © 2011 by Springer Science+Business Media, LLC
Subject
Physics; Theoretical, Mathematical and Computational Physics; Statistical Physics, Dynamical Systems and Complexity; Physical Chemistry ; Quantum Physics
ISSN
0022-4715
eISSN
1572-9613
DOI
10.1007/s10955-011-0177-z
Publisher site
See Article on Publisher Site

Abstract

Properties of Random Overlap Structures (ROSt)’s constructed from the Edwards-Anderson (EA) Spin Glass model on ℤ d with periodic boundary conditions are studied. ROSt’s are ℕ×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.

Journal

Journal of Statistical PhysicsSpringer Journals

Published: Mar 22, 2011

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