Spin-Glass Stochastic Stability: a Rigorous Proof

Details Spin-Glass Stochastic Stability: a Rigorous Proof Spin-Glass Stochastic Stability: a Rigorous Proof

2004-08-02

arxiv.org/abs/math-ph/0408002v2

Physics

Mathematical Physics

12 pages, revised version

Scientific paper

10.1007/s00023-005-0229-5

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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