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
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submitted 13/10/04, accepted 22/11/04
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Contucci, P., Giardinà, C. Spin-Glass Stochastic Stability: a Rigorous Proof. Ann. Henri Poincaré 6, 915–923 (2005). https://doi.org/10.1007/s00023-005-0229-5
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DOI: https://doi.org/10.1007/s00023-005-0229-5