Statistical Field Theory (Horgan)

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1、StatisticalFieldTheoryRRHorganNovember26,2010Contents1BOOKSiii2Introduction13Definitions,NotationandStatisticalPhysics24TheD=1Isingmodelandthetransfermatrix75ThePhenomenologyofPhaseTransitions105.1Thegeneralstructureofphasediagrams.............165.1.1Structuresinapha

2、sediagram:adescriptionofQ...166Landau-Ginsburgtheoryandmeanfieldtheory187Meanfieldtheory228Thescalinghypothesis259Criticalpropertiesofthe1DIsingmodel2810Theblockingtransformation2911TheRealSpaceRenormalizationGroup3512ThePartitionFunctionandFieldTheory4513TheGaussianM

3、odel47iCONTENTSii14ThePerturbationExpansion5115TheGinsbergCriterionforDc5916CalculationoftheCriticalIndex6017GeneralIdeas6717.1DomainsandtheMaxwellConstruction.................6717.2Typesofcriticalpoint..........................6817.3Hysteresis......................

4、...........7017.4MeanFieldTheory............................711BOOKSiii1BOOKS(1)“StatisticalMechanicsofPhaseTransitions”J.M.Yeomans,OxfordScientificPublications.(2)“StatisticalPhysics”,LandauandLifshitz,PergammonPress.(3)“TheTheoryofCriticalPhenomena”J.J.Binneyetal.,

5、OxfordScientificPub-lications.(4)“ScalingandRenormalizationinStatisticalPhysics”JohnCardy,CambridgeLectureNotesinPhysics.(5)“QuantumandStatisticalFieldTheory”M.LeBellac,ClarendonPress.(6)“IntroductiontotheRenormalisationGroupofCriticalPhenomena”P.PfeutyandG.Toulouse,

6、Wiley.‘(7)“FluctuationTheoryofphaseTransitions”PatashinskiiandPokrovskii,Perg-amon.(8)“FieldTheorytherenormalisationGroupandCriticalPhenomena”D.Amit,McGaw-Hill.(*9)“QuantumFieldTheoryofCriticalPhenomena”J.Zinn-Justin,OXFORD.(*10)“PhaseTransitionsandCriticalPhenomena

7、”inmanyvolumes,editedbyC.DombandM.Green/Lebowitz.(*11)“StatisticalFieldTheory”VolsIandII,ItzyksonandDrouffe,CUP.Note*meansit’saharderbook.2INTRODUCTION12IntroductionAgeneralprobleminphysicsistodeducethemacroscopicpropertiesofaquantumsystemfromamicroscopicdescription.

8、Suchsystemscanonlybedescribedmathe-maticallyonascalemuchsmallerthanthescaleswhichareprobedexperimentallyoronwhichthesystemnaturallyinterac