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 <sup>-1</sup>. 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. © 2005 Birkhäuser Verlag, Basel, Switzerland.

Spin-glass stochastic stability: A rigorous proof / P., Contucci; Giardina', Cristian. - In: ANNALES HENRI POINCARE'. - ISSN 1424-0637. - ELETTRONICO. - 6:(2005), pp. 915-923. [10.1007/s00023-005-0229-5]

Spin-glass stochastic stability: A rigorous proof

GIARDINA', Cristian
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. © 2005 Birkhäuser Verlag, Basel, Switzerland.
2005
6
915
923
Spin-glass stochastic stability: A rigorous proof / P., Contucci; Giardina', Cristian. - In: ANNALES HENRI POINCARE'. - ISSN 1424-0637. - ELETTRONICO. - 6:(2005), pp. 915-923. [10.1007/s00023-005-0229-5]
P., Contucci; Giardina', Cristian
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/639601
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