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      Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model

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          Abstract

          By using a simple interpolation argument, in previous work we have proven the existence of the thermodynamic limit, for mean field disordered models, including the Sherrington-Kirkpatrick model, and the Derrida p-spin model. Here we extend this argument in order to compare the limiting free energy with the expression given by the Parisi Ansatz, and including full spontaneous replica symmetry breaking. Our main result is that the quenched average of the free energy is bounded from below by the value given in the Parisi Ansatz uniformly in the size of the system. Moreover, the difference between the two expressions is given in the form of a sum rule, extending our previous work on the comparison between the true free energy and its replica symmetric Sherrington-Kirkpatrick approximation. We give also a variational bound for the infinite volume limit of the ground state energy per site.

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          Author and article information

          Journal
          07 May 2002
          Article
          10.1007/s00220-002-0773-5
          cond-mat/0205123
          Custom metadata
          Communications in Mathematical Physics, Volume 233, Issue 1, pp. 1-12 (2003)
          16 pages
          cond-mat.dis-nn cond-mat.stat-mech math-ph math.MP

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