统计场论（第1卷）

图书标准信息

• 作者 Claude、Jean-Michel Drouffe 编
• 出版社 世界图书出版公司
• 出版时间 2004-11
• 版次 1
• ISBN 9787506266420
• 定价 72.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 403页

【内容简介】

Sometenyearsago,whencompletingwithJ.-B.ZuberaprevioustextonQuantumFieldTheory,theseniorauthorwaspainfullyawarethatlittlementionwasmadethatmethodsinstatisticalphysicsandEuclideanfieldtheorywerecomingcloserandcloser,withcommontoolsbasedontheuseofpathintegralsandtherenormalizationgroupgivinginsightsonglobalstructures.Itwaspartlytofillthisgapthatthepresentbookwasundertaken.Alas,overthefiveyearsthatittooktocometolife,bothsubjectshaveundergoneanewevolution.Disorderedmedia,growthpatterns,complexdynamicalsystemsorspinglassesareamongthenewimportanttopicsinstatisticalmechanics,whilesuperstringtheoryhasturnedtothestudyofextendedsystems,Kaluza-Kleintheoriesinhigherdimensions,anticommutingcoordinates...inanattempttoformulateaunifiedmodelincludingallknowninteractions.Newandsophisticatedtechniqueshaveinvadedstatisticalphysics,rangingfromalgebraicmethodsinintegrablesystemstofractalsetsorrandomsurfaces.Powerfulcomputersorspecialdevicesprovide"experimental"meansforanewbrandoftheoreticalphysicists.Inquantumfieldtheory,applicationsofdifferentialtopology,geometry,Riemannianmanifolds,operatortheory...requireadeeperbackgroundinmathematicsandaknowledgeofsomeofitsmostrecentdevelopments.Asaresult,whensurveyingwhathasbeenincludedinthepresentvolumeinanattempttouncoverthebasicunityofthesesubjects,theauthorshavethesameunsatisfactoryfeelingofnotbeingabletobringthereaderreallyuptodate.Itispresumablythefateofsuchendeavourstoalwayscomeshortofaccomplishingtheirpurpose.

【目录】

ContentsofVolume2
Preface
1FromBrownianmotiontoEuclideanfields
1.1Brownianmotion
1.1.1Randomwalks
1.1.2Thesumoverpaths
1.1.3ThedimensiontwoofBrowniancurves
1.2Euclideanfields
1.2.1Freefields
1.2.2Interactingfieldsandrandomwalks
1.2.3Self-avoidingwalksandthelimitn→0
1.2.4Comparisonwiththehightemperatureexpansion
1.2.5Theone-dimensionalcase
1.ALattices
Notes

2Grassmannianintegralsandthetwo-dimensionalIsingmodel
2.1Grassmannianintegrals
2.1.1Anticommutingvariables
2.1.2Integrals
2.2Thetwo-dimensionalIsingmodel
2.2.1Duality
2.2.2Transfermatrix
2.2.3Fermionicrepresentation
2.2.4Freeenergy
2.2.5Spontaneousmagnetization
2.2.6Correlationfunctioninthehightemperaturephase
2.2.7Surfacetension
2.3Criticalcontinuoustheory
2.3.1Effectiveaction
2.3.2Correlationfunctions
2.AQuadraticdifferencesandPainleveequationsNotes

3Spontaneoussymmetrybreaking,meanfield
3.1Meanfieldapproximation
3.1.1Dielectriccoastantofapolarizablemedium
3.1.2Classicalspinmodelwithafinitesymmetrygroup
3.1.3Continuoussymmetrygroup
3.1.4TheBetheapproximation
3.1.5Criticalexponents
3.2Lee-Yangzeroes
3.2.1TheLee-Yangtheorem
3.2.2Theone-dimensionalcase
3.2.3Generalproperties
3.2.4Zeroesinthetemperatureplane
3.3Largenlimit
3.3.1Saddlepointmethod
3.3.2Factorization
3.3.3Couplingtoanexternalfield
3.4Correctionstomeanfield
3.4.1LaplacetransformNotes

4ScalingtransformationsandtheXY-model
4.1Scalinglaws.Realspacerenormalization
4.1.1Homogeneityandscaleinvariance
4.1.2Recurrencerelationsinrealspace
4.1.3Examplesandapproximations
4.2TheXY-model
4.2.1Hightemperaturebehaviour
4.2.2Lowtemperatureexpansion.Vortices
4.2.3TheVillainaction
4.2.4Correlations
4.2.5Renormalizationflow
4.ATwo-dimensionalsystemswithcontinuoussymmetry
4.A.1Magnetizationinequality
4.A.2Correlationinequality
4.BPhenomenologicalrenormalizationNotes

5Continuousfieldtheoryandtherenormalizationgroup
5.1TheLagrangiananddimensionalanalysis
5.1.1Introduction
5.1.2Generatingfunctionalsanddimensionalanalysis
5.2Theperturbativemethod
5.2.1Diagrammaticseries
5.2.2Loopexpansion
5.2.3Evaluationofintegralsanddimensionalcontinuation
5.2.4Grouptheoreticalfactors
5.2.5Powercounting
5.2.6Perturbativcrenormalization
5.3Therenormalizationgroup
5.3.1Renormalizationflow
5.3.2Criticalexponents
5.3.3FromtheGaussianultravioletfixedpointtotheinfraredcriticalpointindimensionlessthanfour
5.3.4Correlationfunctionsatthecriticalpoint
5.3.5Expansionnearthecriticalpoint
5.3.6Scalinglawsbelowthecriticaltemperature
5.4Correctionstoscalinglaws
5.4.1Deviationfromthecriticalpointindimensionlowerthanfour
5.4.2Logarithmiccorrectionsindimensionfour
5.4.3Irrelevantoperators
5.5Numericalresults
5.5.1e-expansionofcriticalexponents
5.5.2Equationofstate
5.5.3Amplituderatios
5.5.4Three-dimensionalresults
5.AMulticriticalpointsNotes

6Latticegaugefields
6.1Generalities
6.1.1Presentation
6.1.2Thecontinuouslimit
6.1.3OrderparameterandElitzur''stheorem
6.1.4Duality
6.2Structureofthephasediagram
6.2.1Meanfieldapproximation
6.2.2Correctionstomeanfieldandrestorationofgaugeinvariance
6.2.3Discretegroups:1/dexpansion
6.2.4Continuousgroups:computationofcorrections
6.3Strongcouplingexpansions
6.3.1Convergence
6.3.2Characterexpansions
6.3.3Freeenergy
6.3.4Stringtensionandrougheningtransition
6.3.5Massspectrum
6.4Latticefermions
6.4.1Thedoublingproblem
6.4.2TheNielsen-Ninomiyatheorem
6.4.3Staggeredfermions
Notes
Index