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      Construction of pure states in mean field models for spin glasses

      Probability Theory and Related Fields
      Springer Nature

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          The Parisi formula

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            General properties of overlap probability distributions in disordered spin systems. Toward Parisi ultrametricity

            For a very general class of probability distributions in disordered Ising spin systems, in the thermodynamical limit, we prove the following property for overlaps among real replicas. Consider the overlaps among s replicas. Add one replica s+1. Then, the overlap q(a,s+1) between one of the first s replicas, let us say a, and the added s+1 is either independent of the former ones, or it is identical to one of the overlaps q(a,b), with b running among the first s replicas, excluding a. Each of these cases has equal probability 1/s.
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              Free energy of the spherical mean field model

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                Author and article information

                Journal
                Probability Theory and Related Fields
                Probab. Theory Relat. Fields
                Springer Nature
                0178-8051
                1432-2064
                November 2010
                November 2009
                : 148
                : 3-4
                : 601-643
                Article
                10.1007/s00440-009-0242-6
                77b47b20-4aa1-4aa6-b0ad-76ac1182830b
                © 2010
                History

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