Statistical field theory: an introduction to exactly solved models in statistical physics
Fundamental concepts of phase transitions, such as order parameters, spontaneous symmetry breaking, scaling transformations, conformal symmetry and anomalous dimensions, have deeply changed the modern vision of many areas of physics, leading to remarkable developments in statistical mechanics, eleme...
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| Format: | Buch |
| Sprache: | English |
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Oxford, United Kingsdom
Oxford University Press
2020
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| Ausgabe: | Second edition |
| Schriftenreihe: | Oxford graduate texts
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| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | Fundamental concepts of phase transitions, such as order parameters, spontaneous symmetry breaking, scaling transformations, conformal symmetry and anomalous dimensions, have deeply changed the modern vision of many areas of physics, leading to remarkable developments in statistical mechanics, elementary particle theory, condensed matter physics and string theory. This self-contained book provides a thorough introduction to the fascinating world of phase transitionsand frontier topics of exactly solved models in statistical mechanics and quantum field theory, such as renormalization groups, conformal models, quantum integrable systems, duality, elastic S-matrices, thermodynamic Bethe ansatz and form factor theory. The clear discussion of physical principles isaccompanied by a detailed analysis of several branches of mathematics distinguished for their elegance and beauty, including infinite dimensional algebras, conformal mappings, integral equations and modular functions. Besides advanced research themes, the book also covers many basic topics in statistical mechanics, quantum field theory and theoretical physics. Each argument is discussed in great detail while providing overall coherent understanding of physical phenomena. Mathematical background is made available in supplements at the end of each chapter, when appropriate. The chapters include problems of different levels of difficulty. Advanced undergraduate and graduate students will find this book a richand challenging source for improving their skills and for attaining a comprehensive understanding of the many facets of the subject |
| Beschreibung: | xxix, 986 Seiten Illustrationen, Diagramme |
| ISBN: | 9780198788102 |
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Contents Part 1 Preliminary Notions 1 Introduction 1.1 Phase Transitions 1.2 The Ising Model 1.3 Ernst Ising Appendix l.A. Ensembles in Classical Statistical Mechanics Appendix l.B. Ensembles in Quantum Statistical Mechanics Problems 2 One-dimensional Systems 2.1 Recursive Approach 2.2 Transfer Matrix 2.3 Series Expansions 2.4 Critical Exponents and Scaling Laws 2.5 The Potts Model 2.6 Models with O(n) Symmetry 2.7 Models with Zn Symmetry 2.8 Feynman Gas Appendix 2.A. Special Functions Appendix 2.B. n-dimensional Solid Angle Appendix 2.C. The Four-colour Problem Problems 3 Approximate Solutions 3.1 Mean Field Theory of the Ising Model 3.2 Mean Field Theory of the Potts Model 3.3 Bethe-Peierls Approximation 3.4 The Gaussian Model 3.5 The spherical model Appendix 3.A. The Saddle Point Method Appendix 3.B. Brownian Motion on a Lattice Problems 3 4 19 21 22 27 41 48 48 55 64 66 67 73 81 84 86 93 95 102 106 106 112 116 120 130 137 141 154
xxiv Part 2 Contents Bi-dimensional Lattice Models 4 Duality of the Two-dimensional Ising Model 4.1 Peierls Argument 4.2 Duality Relation in Square Lattices 4.3 Duality Relation: Hexagonal and Triangular Lattices 4.4 Star-triangle Identity 4.5 Ising Model Critical Temperature: Triangle and Hexagonal Lattices 4.6 Duality in Two Dimensions Appendix 4.A. Numerical Series Appendix 4.B. Poisson Sum Formula Problems 5 Combinatorial Solutions of the Ising Model 5.1 Combinatorial Approach 5.2 Dimer Method Problems 6 Transfer Matrix of the Two-dimensional Ising Model 6.1 Baxter’s Approach 6.2 Eigenvalue Spectrum at the Critical Point 6.3 Away from the Critical Point 6.4 Yang-Baxter Equation and R-matrix Problems Part 3 161 162 163 170 172 174 176 183 184 186 189 189 200 209 211 212 223 227 227 233 Quantum Field Theory and Conformal Invariance 7 Quantum Field Theory 7.1 Motivations 7.2 Order Parameters and Lagrangian 7.3 Field Theory of the Ising Model 7.4 Correlation Functions and Propagator 7.5 Perturbation Theory and Feynman Diagrams 7.6 Legendre Transformation and Vertex Functions 7.7 Spontaneous Symmetry Breaking and Multi-criticality 7.8 Renormalization 7.9 Field Theory in Minkowski Space 7.10 Particles 7.11 Correlation Functions and Scattering Processes Appendix 7.A. Feynman Path Integral Formulation Appendix 7.B. Relativistic Invariance Appendix 7.C. Noether Theorem Problems 237 237 239 243 246 250 256 259 264 267 272 276 278 280 283 285
Contents XXV Renormalization Group 289 8.1 Introduction 8.2 Reducing the Degrees of Freedom 8.3 Transformation Laws and Effective Hamiltonians 8.4 Fixed Points 8.5 The Ising Model 8.6 The Gaussian Model 8.7 Operators and Quantum Field Theory 8.8 Functional Form of the Free Energy 8.9 Critical Exponents and Universal Ratios 8.10 ^-Functions Problems 289 291 292 296 300 303 304 307 309 313 317 Fermionic Formulation of the Ising Model 319 9.1 Introduction 9.2 Transfer Matrix and Hamiltonian Limit 9.3 Order and Disorder Operators 9.4 Perturbation Theory 9.5 Expectation Values of Order and Disorder Operators 9.6 Diagonalization of the Hamiltonian 9.7 Dirac Equation Problems 319 320 325 327 329 331 336 339 Conformal Field Theory 341 10.1 Introduction 10.2 The Algebra of Local Fields 10.3 Conformal Invariance 10.4 Quasi-primary Fields 10.5 Two-dimensional Conformal Transformations 10.6 Ward Identity and Primary Fields 10.7 Central Charge and Virasoro Algebra 10.8 Representation Theory 10.9 Hamiltonian on a Cylinder Geometry and Casimir Effect 10.10 Entanglement Entropy Appendix 10.A. Moebius Transformations Problems 341 342 347 351 353 358 362 368 378 381 386 395 Minimal Conformal Models 399 11.1 11.2 11.3 Introduction Null Vectors and Kac Determinant Unitary Representations 399 400 403
xxvi Contents 11.4 Minimal Models 11.5 Coulomb Gas 11.6 Landau-GinzburgFormulation 11.7 Modular Invariance Appendix 11 .A. Hypergeometric functions Problems 405 412 425 429 437 440 Conformal Field Theory of Free Bosonic andFermionic Fields 443 12.1 Introduction 12.2 Conformal Field Theory of Free Bosonic Fields 12.3 Conformal Field Theory of a FreeFermionic Field 12.4 Bosonization Problems 443 443 455 467 471 13 Conformal Field Theories with ExtendedSymmetries 476 12 13.1 Introduction 13.2 Superconformai Models 13.3 Parafermion Models 13.4 Кас-Moody Algebra 13.5 Conformal Models as Cosets Appendix 13.A. Lie Algebra Problems 14 The Arena of Conformal Models 14.1 Introduction 14.2 The Ising Model 14.3 The Universality Class of the Tricritical Ising Model 14.4 3-state Potts Model 14.5 The Yang-Lee Model 14.6 Conformal Models with O(n)Symmetry Problems 476 476 482 489 502 505 516 518 518 518 530 533 537 539 542 Part 4 Away from Criticality 15 In the Vicinity of the Critical Points 15.1 15.2 15.3 15.4 15.5 15.6 15.7 Introduction Conformal Perturbation Theory Example: The Two-point Function of the Yang-Lee model Renormalization Group and B-functions c-theorem Applications of the c theorem Δ theorem 545 545 548 554 556 552 555 572
Contents 16 Integrable Quantum Field Theories 16.1 Introduction 16.2 The Sinh-Gordon Model 16.3 The Sine-Gordon Model 16.4 The Bullogh-Dodd Model 16.5 Integrability versus Non-integrability 16.6 The Toda Field Theories 16.7 Toda Field Theories with Imaginary Coupling Constant 16.8 Deformation of Conformal Conservation Laws 16.9 Multiple Deformations of Conformal Field Theories Problems 17 S-matrix Theory 17.1 Analytic Scattering Theory 17.2 General Properties of Purely Elastic Scattering Matrices 17.3 Unitarity and Crossing Invariance Equations 17.4 Analytic Structure and Bootstrap Equations 17.5 Conserved Charges and Consistency Equations Appendix 17.A. Historical Developments of the S-matrix Theory Appendix 17.B. Scattering Processes in Quantum Mechanics Appendix 17.C. и-particle Phase Space Problems 18 Exact S-matrices Yang-Lee and Bullogh-Dodd Models Ф1,з Integrable Deformation of the Conformal Minimal Models Л12,2п+з 680 18.3 Multiple Poles 18.4 S-matrices of the Ising Model 18.5 The Tricritical Ising Model at T T 18.6 Thermal Deformation of the 3-state PottsModel 18.7 General Expression Toda Field Theories 18.8 Non-relativistic Limit of Toda Field Theories 18.9 Models with Internal O(n) Invariance 18.10 S-matrix of the Sine-Gordon Model 18.11 S-matrices for Φι,3, Φι,23 Фг,1 Deformation of Minimal Models 18.12 Elastic SUSY S-matrix Problems 18.1 18.2 19 Form Factors and Correlation Functions 19.1 19.2 General Properties of the Form Factors Watson’s Equations xxvii 575 575 576 582 588 590 593 604 606 615 619 622 623 634 641 646 651 655 659 664 672 676 676 682 684 692
696 700 701 704 710 715 730 739 744 745 748
xxviii Contents 19.3 19.4 19.5 19.6 19.7 19.8 Recursive Equations The Operator Space Correlation Functions Form Factors of the Stress-energy Tensor Vacuum Expectation Values Ultraviolet Limit 19.9 The Ising Model at T+T 19.10 Form Factors of the Sinh-Gordon Model 19.11 The Ising Model in a Magnetic Field Problems Part 5 Finite Size Effects 20 Thermodynamic Bethe Ansatz 21 751 752 754 757 759 763 766 772 780 785 791 20.1 Introduction 20.2 Casimir Energy 20.3 Bethe Relativistic Wave Function 20.4 Derivation of Thermodynamics 20.5 The Meaning of Pseudo-energy 20.6 Infrared and Ultraviolet Limits 20.7 The Coefficient of Bulk Energy 20.8 The General Form of the TBA Equations 20.9 The Exact Relation λ(m) 20.10 Examples 20.11 Thermodynamics of the Free Field Theories 20.12 L-channel Quantization 20.13 LeClair-Mussardo Formula Problems 791 791 794 796 803 806 808 811 814 817 821 822 828 834 Boundary Field Theory 836 21.1 21.2 21.3 21.4 21.5 21.6 21.7 21.8 Introduction Stress-energy Tensor in Boundary CFT Conformal Boundary Operators Conformal Boundary States Operator Product Expansion Involving a Boundary Operator Massive Integrable Boundary Field Theory Boundary States Massive Boundary Ising Model Correlation Functions Problems 21.9 836 837 839 842 847 848 850 851 854 858
Contents Part 6 Non-Integrable Aspects 22 Form Factor Perturbation Theory 22.1 Breaking Integrability 22.2 Multiple Deformations of the Conformal Field Theories 22.3 Form Factor Perturbation Theory 22.4 First-order Perturbation Theory 22.5 Non-locality and Confinement of the Excitations 22.6 Multi-frequency Sine-Gordon Model Problems 23 Particle Spectrum by Semi-classical Methods 23.1 Introduction 23.2 Kinks 23.3 A Semi-classical Formula for the Kink Matrix Elements 23.4 Universal Mass Formula 23.5 Symmetric Wells 23.6 Asymmetric Wells 23.7 Double Sine-Gordon Model Problems 24 Interacting Fermions and Supersymmetric Models 24.1 Introduction 24.2 Fermion in a Bosonic Background 24.3 The Fermionic Bound States in T = 0Sector 24.4 Symmetric Wells 24.5 Supersymmetric Theory 24.6 General Results in SUSY Theories 24.7 Integrable SUSY Models 24.8 Non-integrable Multi-frequency Super Sine-Gordon Models 24.9 Phase Transition and Meta-stable States 24.10 Summary Problems 25 Truncated Hilbert Space Approach 25.1 Truncated Hamiltonians of Quantum Mechanics 25.2 Truncated Hamiltonian of the Deformed Conformal Models 25.3 Finite-size Mass Corrections 25.4 The Scaling Region of the Ising Model Problems Index xxix 863 863 865 867 871 874 876 880 882 882 883 888 890 893 897 901 910 913 913 914 918 921 923 925 927 930 933 937 939 943 944 951 962 964 973 975 |
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| spelling | Mussardo, Giuseppe Verfasser (DE-588)140219064 aut Statistical field theory an introduction to exactly solved models in statistical physics Giuseppe Mussardo, SISSA (Scuola Internazionale Superiore di Studi Avanzati), Trieste Second edition Oxford, United Kingsdom Oxford University Press 2020 xxix, 986 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Oxford graduate texts Fundamental concepts of phase transitions, such as order parameters, spontaneous symmetry breaking, scaling transformations, conformal symmetry and anomalous dimensions, have deeply changed the modern vision of many areas of physics, leading to remarkable developments in statistical mechanics, elementary particle theory, condensed matter physics and string theory. This self-contained book provides a thorough introduction to the fascinating world of phase transitionsand frontier topics of exactly solved models in statistical mechanics and quantum field theory, such as renormalization groups, conformal models, quantum integrable systems, duality, elastic S-matrices, thermodynamic Bethe ansatz and form factor theory. The clear discussion of physical principles isaccompanied by a detailed analysis of several branches of mathematics distinguished for their elegance and beauty, including infinite dimensional algebras, conformal mappings, integral equations and modular functions. Besides advanced research themes, the book also covers many basic topics in statistical mechanics, quantum field theory and theoretical physics. Each argument is discussed in great detail while providing overall coherent understanding of physical phenomena. Mathematical background is made available in supplements at the end of each chapter, when appropriate. The chapters include problems of different levels of difficulty. Advanced undergraduate and graduate students will find this book a richand challenging source for improving their skills and for attaining a comprehensive understanding of the many facets of the subject bicssc / Quantum physics (quantum mechanics & quantum field theory) bicssc / Mathematical physics bicssc / Materials / States of matter bicssc / Particle & high-energy physics bicssc / Condensed matter physics (liquid state & solid state physics) bicssc / Physics Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf Statistische Mechanik (DE-588)4056999-8 s Quantenfeldtheorie (DE-588)4047984-5 s DE-604 Erscheint auch als Online-Ausgabe 978-0-19-183008-2 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031726132&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mussardo, Giuseppe Statistical field theory an introduction to exactly solved models in statistical physics bicssc / Quantum physics (quantum mechanics & quantum field theory) bicssc / Mathematical physics bicssc / Materials / States of matter bicssc / Particle & high-energy physics bicssc / Condensed matter physics (liquid state & solid state physics) bicssc / Physics Quantenfeldtheorie (DE-588)4047984-5 gnd Statistische Mechanik (DE-588)4056999-8 gnd |
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| title | Statistical field theory an introduction to exactly solved models in statistical physics |
| title_auth | Statistical field theory an introduction to exactly solved models in statistical physics |
| title_exact_search | Statistical field theory an introduction to exactly solved models in statistical physics |
| title_full | Statistical field theory an introduction to exactly solved models in statistical physics Giuseppe Mussardo, SISSA (Scuola Internazionale Superiore di Studi Avanzati), Trieste |
| title_fullStr | Statistical field theory an introduction to exactly solved models in statistical physics Giuseppe Mussardo, SISSA (Scuola Internazionale Superiore di Studi Avanzati), Trieste |
| title_full_unstemmed | Statistical field theory an introduction to exactly solved models in statistical physics Giuseppe Mussardo, SISSA (Scuola Internazionale Superiore di Studi Avanzati), Trieste |
| title_short | Statistical field theory |
| title_sort | statistical field theory an introduction to exactly solved models in statistical physics |
| title_sub | an introduction to exactly solved models in statistical physics |
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