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      About the overlap distribution in mean field spin glass models

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          Abstract

          We continue our presentation of mathematically rigorous results about the Sherrington-Kirkpatrick mean field spin glass model. Here we establish some properties of the distribution of overlaps between real replicas. They are in full agreement with the Parisi accepted picture of spontaneous replica symmetry breaking. As a byproduct, we show that the selfaveraging of the Edwards-Anderson fluctuating order parameter, with respect to the external quenched noise, implies that the overlap distribution is given by the Sherrington-Kirkpatrick replica symmetric Ansatz. This extends previous results of Pastur and Shcherbina. Finally, we show how to generalize our results to realistic short range spin glass models.

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          Solvable Model of a Spin-Glass

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            Author and article information

            Journal
            12 December 2012
            Article
            10.1142/S0217979296000751
            1212.2919
            95347bb3-fa9f-4d02-8c6b-51bc8b2f02d2

            http://arxiv.org/licenses/nonexclusive-distrib/1.0/

            History
            Custom metadata
            International Journal of Modern Physics B 10, 1675-1684 (1996)
            11 pages
            cond-mat.dis-nn math-ph math.MP

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