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Spin-Glass Stochastic Stability: a Rigorous Proof

P. Contucci·C. Giardina'
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Abstract

We prove the property of stochastic stability previously introduced as a consequence of the (unproved) continuity hypothesis in the temperature of the spin-glass quenched state. We show that stochastic stability holds in beta-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 applyed to the thermal fluctuations only.

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P. Contucci, C. Giardina'. 2004-10-12. Spin-Glass Stochastic Stability: a Rigorous Proof. https://doi.org/10.1007/s00023-005-0229-5

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