NDLI: Spin-Glass Stochastic Stability: a Rigorous Proof

Content Provider	Springer Nature Link
Author	Contucci, Pierluigi Giardinà, Cristian
Copyright Year	2005
Abstract	We prove the property of stochastic stability previously introduced as a consequence of the (unproved) continuity hypothesis in the temperature of the spinglass quenched state. We show that stochastic stability holds in β-average for both the Sherrington-Kirkpatrick model in terms of the square of the overlap function and for the Edwards-Anderson model in terms of the bond overlap. We show that the volume rate at which the property is reached in the thermodynamic limit is V−1. As a byproduct we show that the stochastic stability identities coincide with those obtained with a different method by Ghirlanda and Guerra when applied to the thermal fluctuations only.Communicated by Jennifer Chayes
Starting Page	915
Ending Page	923
Page Count	9
File Format	PDF
ISSN	14240637
Journal	Annales Henri Poincaré
Volume Number	6
Issue Number	5
e-ISSN	14240661
Language	English
Publisher	Birkhäuser-Verlag
Publisher Date	2005-10-05
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Quantum Physics Elementary Particles, Quantum Field Theory Relativity and Cosmology Dynamical Systems and Ergodic Theory Mathematical and Computational Physics Mathematical Methods in Physics
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Nuclear and High Energy Physics Mathematical Physics

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Spin-Glass Stochastic Stability: a Rigorous Proof