statistical physics of spin glasses and information processing an introduction - nishimori h.

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1、StatisticalPhysicsofSpinGlassesandInformationProcessingAnIntroductionHIDETOSHINISHIMORIDepartmentofPhysicsTokyoInstituteofTechnologyCLARENDONPRESS.OXFORD2001StatisticalPhysicsofSpinGlassesandInformationProcessingAnIntroductionHidetoshiNishimori,DepartmentofPhysics,TokyoInstituteofTechnology,Japan•On

2、eofthefewbooksinthisinterdisciplinaryarea•Rapidlyexpandingfield•Up-to-datepresentationofmodernanalyticaltechniques•Self-containedpresentationSpinglassesaremagneticmaterials.Statisticalmechanicshasbeenapowerfultooltotheoreticallyanalysevariousuniquepropertiesofspinglasses.Anumberofnewanalyticaltechni

3、queshavebeendevelopedtoestablishatheoryofspinglasses.Surprisingly,thesetechniqueshaveofferednewtoolsandviewpointsfortheunderstandingofinformationprocessingproblems,includingneuralnetworks,error-correctingcodes,imagerestoration,andoptimizationproblems.Thisbookisoneofthefirstpublicationsofthepasttenye

4、arsthatprovidesabroadoverviewofthisinterdisciplinaryfield.Mostpartofthebookiswritteninaself-containedmanner,assumingonlyageneralknowledgeofstatisticalmechanicsandbasicprobabilitytheory.Itprovidesthereaderwithasoundintroductiontothefieldandtotheanalyticaltechniquesnecessarytofollowitsmostrecentdevelo

5、pments.Contents:Mean-fieldtheoryofphasetransitions;Mean-fieldtheoryofspinglasses;Replicasymmetrybreaking;Gaugetheoryofspinglasses;Error-correctingcodes;Imagerestoration;Associativememory;Learninginperceptron;Optimizationproblems;A.EigenvaluesoftheHessian;B.Parisiequation;C.Channelcodingtheorem;D.Dis

6、tributionandfreeenergyofK-Sat;References;Index.InternationalSeriesofMonographsonPhysicsNo.111,OxfordUniversityPressPaperback,£24.95,0-19-850941-3Hardback,£49.50,0-19-850940-5August2001,285pages,58linefigures,2halftonesPREFACEThescopeofthetheoryofspinglasseshasbeenexpandingwellbeyonditsorigi-nalgoalo

7、fexplainingtheexperimentalfactsofspinglassmaterials.Forthefirsttimeinthehistoryofphysicswehaveencounteredanexplicitexampleinwhichthephasespaceofthesystemhasanextremelycomplexstructureandyetisamenableto