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1、IntroductiontoConformalInvarianceinStatisticalMechanicsandtoRandomSurfaceModelsFrancoisDavidServicedePhysiqueTh@orique,CESaclay91191Gif-sur-YvetteCedex,France1IntroductionInthefirstpartoftheselecturesIgiveabriefandsomewhatsuperficialintro-ductiontothetechniquesofconformalinvar
2、ianceandtoafewapplicationsinstatisticalmechanicsintwodimensions.Mypurposeistointroducethebasicideasandsomestandardresultsforthestudentswhoarenotfamiliarwiththetheory,andtointroduceconceptsandtoolswhichwillbeusefulfortheotherlecturers,ratherthantogiveacompleteanduptodatereviewo
3、fthesubject.Therearenowseveralverygoodandcompletesetsoflecturenotes,reviewpa-persandbooksavailable,includingtheseminalpaperbyBelavin,PolyakovandZamolochikov(Belavinetal.(1984)),andthecontentoftheselectureswillbebynomeanoriginal.MostofthematerialisinspiredfromtheLesHouches'88le
4、cturesbyP.Ginsparg(Ginsparg(1989))andbyJ.Cardy(Cardy(1989)),andfromsomelecturesnotesbyP.DiFrancesco,P.MathieuandD.Senechal(DiFrancescoetal.(1994)).FurtherbibliographicinformationisprovidedbyCardy(1987),Dotsenko(1988),ChristeandHenkel(1993),Itzyksonetal.(1988).InthesecondpartId
5、iscussseveralproblemsinthestatisticalmechanicsoftwodimensionalrandomsurfacesandmembranes.Asanintroduction,Ipresentsomebasicfactsaboutthestatisticalmechanicsofone-dimensionalobjectsandpolymers,whichareclassicalexamplesofobjectswithcriticalproperties.ThenIemphasizethespecialrole
6、ofcurvatureenergyandoftheelasticenergyassoci-atedwiththeinternalstructureofmembranes,andthecorrespondingmodelsofrandomsurfaces.Finally,Idiscussthespecificproblemofself-avoidingtetheredsurfaces,whosecriticalpropertiesarestillpoorlyunderstood,andforwhichtheapplicabilityofsomebas
7、ictechniquesoffieldtheory,suchasrenormalizationgroupcalculations,hasbeenunderstoodonlyrecently.Iamverygratefultotheorganizers,andespeciallyH.GeyerandE.Pheiffer,andtoallitsparticipantformakingthisschoolsosuccessful.2FranqoisDavid2IntroductiontoConformalInvarianceinStatisticalMe
8、chanics2.1RenormallzationGroup,ScaleandConformalInvarianeeCri
