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Spin Glasses: Statics and DynamicsChaos in Mean-field Spin-glass Models

Spin Glasses: Statics and Dynamics: Chaos in Mean-field Spin-glass Models [Physicists understand mean-field spin-glass models as possessing a complex free-energy landscape with many equilibrium states. The problem of chaos concerns the evolution of this landscape upon changing the external parameters of the system and is considered relevant for the interpretation of important features of real spin-glass and for understanding the performance of numerical algorithms. The subject is strongly related to that of constrained systems which is considered by mathematicians the natural framework for proving rigorously some of the most peculiar properties of Parisi’s replicasymmetry-breaking solution of mean-field spin-glass models, notably ultrametricity. Many aspects of the problems turned out to possess an unexpected level of difficulty and are still open. We present the results of the physics literature on the subject and discuss the main unsolved problems from a wider perspective.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Spin Glasses: Statics and DynamicsChaos in Mean-field Spin-glass Models

Part of the Progress in Probability Book Series (volume 62)
Editors: de Monvel, Anne Boutet; Bovier, Anton
Rizzo, Tommaso
Spin Glasses: Statics and Dynamics — Dec 14, 2009
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14 pages

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References (14)

Publisher
Birkhäuser Basel
Copyright
© Birkhäuser Basel 2009
ISBN
978-3-7643-8999-4
Pages
143 –157
DOI
10.1007/978-3-7643-9891-0_6
Publisher site
See Chapter on Publisher Site

Abstract

[Physicists understand mean-field spin-glass models as possessing a complex free-energy landscape with many equilibrium states. The problem of chaos concerns the evolution of this landscape upon changing the external parameters of the system and is considered relevant for the interpretation of important features of real spin-glass and for understanding the performance of numerical algorithms. The subject is strongly related to that of constrained systems which is considered by mathematicians the natural framework for proving rigorously some of the most peculiar properties of Parisi’s replicasymmetry-breaking solution of mean-field spin-glass models, notably ultrametricity. Many aspects of the problems turned out to possess an unexpected level of difficulty and are still open. We present the results of the physics literature on the subject and discuss the main unsolved problems from a wider perspective.]

Published: Dec 14, 2009

Keywords: 82-06; 82D30; Spin-glass; chaos; constrained systems; replica method

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