Mean Field Model Spin Glasses-Talagrand

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1、MichelTALAGRANDMeanFieldModelsforSpinGlassesVolumeI:BasicExamplesSeptember14,2010Springer-VerlagBerlinHeidelbergNewYorkLondonParisTokyoHongKongBarcelonaBudapestVToWansooT.Rhee,forsomanyreasons.ContentsIntroduction..................................................11.TheSherrington-KirkpatrickModel.

2、.....................91.1Introduction...........................................91.2Notationsandsimplefacts...............................131.3GaussianInterpolationandtheSmartPathmethod.........201.4Latala’sArgument......................................371.5AKindofCentralLimitTheorem..............

3、..........591.6TheCavityMethod.....................................611.7Gibbs’Measure;theTAPEquations......................751.8SecondMomentComputationsandtheAlmeida-Thoulessline881.9BeyondtheATLine....................................1011.10CentralLimitTheoremfortheOverlaps...................1061.

4、11NonGaussianBehavior:Hanen’sTheorem.................1211.12TheSKModelwithd-componentSpins...................1331.13ThePhysicist’sReplicaMethod..........................1481.14NotesandComments...................................1542.ThePerceptronModel....................................1592.1Introd

5、uction...........................................1592.2TheSmartPath........................................1622.3CavityinM...........................................1682.4TheReplicaSymmetricSolution.........................1812.5ExponentialInequalities.................................1902.6Notesan

6、dComments...................................1983.TheShcherbinaandTirozziModel.......................1993.1ThePowerofConvexity.................................1993.2TheReplica-SymmetricEquations........................2153.3ControllingtheSolutionsoftheRSEquations..............2323.4NotesandComments

7、...................................243VIIIContents4.TheHopfieldModel......................................2454.1Introduction:TheCurie-WeissModel.....................2454.2LocalConvexityandtheHubbard-StratonovitchT