Abstract
AbstractWe give a short overview of the recent rigorous mathematical methods developed for the study of complex disordered systems, in particular spin glasses in the mean field Sherrington-Kirkpatrick formulation. We show that interpolation methods, and related comparison arguments, are very powerful tools in order to study these models. We consider the problem of the infinite volume limit for the free energy, Then we introduce the Parisi solution for the spin glass, based on the spontaneous breaking of replica symmetry, and characterized by a functional order parameter entering in a variational principle. We show how the validity of the Parisi representation can be rigorously established. Finally, we point out some perspective for future developments.KeywordsThermodynamic LimitSpin GlassReplica SymmetryGeneralize Variational PrincipleSpin Glass ModelThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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