Statistical field theory: an introduction to exactly solved models in statistical physics
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2010
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Oxford graduate texts
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XXII, 755 S. Ill., graph. Darst. |
| ISBN: | 9780199547586 |
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| 100 | 1 | |a Mussardo, Giuseppe |e Verfasser |0 (DE-588)140219064 |4 aut | |
| 245 | 1 | 0 | |a Statistical field theory |b an introduction to exactly solved models in statistical physics |c Giuseppe Mussardo |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2010 | |
| 300 | |a XXII, 755 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Oxford graduate texts | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Field theory (Physics) / Statistical methods | |
| 650 | 4 | |a Field theory (Physics) |x Statistical methods | |
| 650 | 0 | 7 | |a Quantenfeldtheorie |0 (DE-588)4047984-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Statistische Mechanik |0 (DE-588)4056999-8 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-017717796 | ||
Datensatz im Suchindex
| _version_ | 1804139355225194496 |
|---|---|
| adam_text | Contents
Part I Preliminary Notions
Introduction
3
1.1
Phase Transitions
3
1.2
The Ising Model
18
1A Ensembles in Classical Statistical
Mechanics
21
IB Ensembles in Quantum Statistical
Mechanics
26
Problems
38
One-dimensional Systems
45
2.1
Recursive Approach
45
2.2
Transfer Matrix
51
2.3
Series Expansions
59
2.4
Critical Exponents and Scaling Laws
61
2.5
The Potts Model
62
2.6
Models with 0{n) Symmetry
67
2.7
Models with Zn Symmetry
74
2.8
Feynman Gas
77
2A Special Functions
78
2B n-dimensional Solid Angle
85
2C The Four-color Problem
86
Problems
94
Approximate Solutions
97
3.1
Mean Field Theory of the Ising Model
97
3.2
Mean Field Theory of the Potts Model
102
3.3
Bethe-Peierls Approximation
105
3.4
The Gaussian Model
109
3.5
The Spherical Model
118
ЗА
The Saddle Point Method
125
3B Brownian Motion on a Lattice
128
Problems
140
Part II
Bidimensional
Lattice Models
Duality of the Two-dimensional Ising Model
147
4.1
Peierls s Argument
148
4.2
Duality Relation in Square Lattices I49
xviii Contents
4.3
Duality
Relation
between Hexagonal and Triangular Lattices
155
4.4
Star-Triangle Identity
157
4.5
Critical Temperature of Ising Model in Triangle and Hexagonal
Lattices
159
4.6
Duality in Two Dimensions
161
4A Numerical Series
167
4B
Poisson Resummation
Formula
168
Problems
170
5
Combinatorial Solutions of the Ising Model
172
5.1
Combinatorial Approach
172
5.2
Dimer Method
182
Problems
191
6
Transfer Matrix of the Two-dimensional Ising Model
192
6.1
Baxters Approach
193
6.2
Eigenvalue Spectrum at the Critical Point
203
6.3
Away from the Critical Point
206
6.4
Yang-Baxter Equation and
Д
-matrix
206
Problems
211
Part III Quantum Field Theory and
Conformai Invariance
7
Quantum Field Theory
217
7.1
Motivations
217
7.2
Order Parameters and Lagrangian
219
7.3
Field Theory of the Ising Model
223
7.4
Correlation Functions and Propagator
225
7.5
Perturbation Theory and Feynman Diagrams
228
7.6
Legendre Transformation and Vertex Functions
234
7.7
Spontaneous Symmetry Breaking and Multicriticality
237
7.8
Renormalization
241
7.9
Field Theory in Minkowski Space
245
7.10
Particles
249
7.11
Correlation Functions and Scattering Processes
252
7A Feynman Path Integral Formulation
254
7B Relativistic
Invariance
256
7C Noether s Theorem
258
Problems
260
8
Renormalization Group
264
8.1
Introduction
264
8.2
Reducing the Degrees of Freedom
266
8.3
Transformation Laws and Effective Hamiltonians
267
8.4
Fixed Points
271
8.5
The Ising Model
273
8.6
The Gaussian Model
277
Contents xix
8.7 Operators and Quantum
Field Theory
278
8.8
Functional Form of the Free Energy
280
8.9
Critical Exponents and Universal Ratios
282
8.10
^-functions
285
Problems
288
9
Fermionic Formulation of the Ising Model
290
9.1
Introduction
290
9.2
Transfer Matrix and Hamiltonian Limit
291
9.3
Order and Disorder Operators
295
9.4
Perturbation Theory
297
9.5
Expectation Values of Order and Disorder Operators
299
9.6
Diagonalization of the Hamiltonian
300
9.7
Dirac Equation
305
Problems
308
10
Conformai
Field Theory
310
10.1
Introduction
310
10.2
The Algebra of Local Fields
311
10.3
Conformai Invariance
315
10.4
Quasi-Primary Fields
318
10.5
Two-dimensional
Conformai
Transformations
320
10.6
Ward Identity and Primary Fields
325
10.7
Central Charge and Virasoro Algebra
329
10.8
Representation Theory
335
10.9
Hamiltonian on a Cylinder Geometry and the
Casimir
Effect
344
10A Moebius Transformations
347
Problems
354
11
Minimal
Conformai
Models
358
11.1
Introduction
358
11.2
Null Vectors and
Кас
Determinant
358
11.3
Unitary Representations
362
11.4
Minimal Models
363
11.5
Coulomb Gas
370
11.6
Landau-Ginzburg Formulation
382
11.7
Modular
Invariance
385
ПА
Hypergeometric Functions
393
Problems
395
12
Conformai
Field Theory of Free Bosonic and Fermionic Fields
397
12.1
Introduction
397
12.2
Conformai
Field Theory of a Free Bosonic Field
397
12.3
Conformai
Field Theory of a Free Fermionic Field
408
12.4
Bosonization
419
Problems
422
xx Contents
13
Conformai
Field Theories with Extended Symmetries
426
13.1
Introduction
426
13.2
Superconformai
Models
426
13.3
Parafermion Models
431
13.4
Kac-Moody Algebra
438
13.5
Conformai
Models as Cosets
448
13A Lie Algebra
452
Problems
462
14
The Arena of
Conformai
Models
464
14.1
Introduction
464
14.2
The Ising Model
464
14.3
The Universality Class of the Tricritical Ising Model
475
14.4
Three-state Potts Model
478
14.5
The Yang-Lee Model
481
14.6
Conformai
Models with O(n) Symmetry
484
Problems
486
Part IV Away from Criticality
15
In the Vicinity of the Critical Points
489
15.1
Introduction
489
15.2
Conformai
Perturbation Theory
491
15.3
Example: The Two-point Function of the Yang-Lee Model
497
15.4
Renormalization Group and ^-functions
499
15.5
C-theorem
504
15.6
Applications of the c-theorem
507
15.7
Δ
-theorein
512
16
Integrable
Quantum Field Theories
516
16.1
Introduction
516
16.2
The Sinh-Gordon Model
517
16.3
The Sine-Gordon Model
523
16.4
The Bullogh- Dodd Model
527
16.5
Integrability versus Non-integrability
530
16.6
The
Toda
Field Theories
532
16.7
Toda
Field Theories with Imaginary Coupling Constant
542
16.8
Deformation of
Conformai
Conservation Laws
543
16.9
Multiple Deformations of
Conformai
Field Theories
551
Problems
555
17
S-Matrix Theory
557
17.1
Analytic Scattering Theory
558
17.2
General Properties of Purely Elastic Scattering Matrices
568
17.3
Unitarity and Crossing
Invariance
Equations
574
17.4
Analytic Structure and Bootstrap Equations
579
17.5
Conserved Charges and Consistency Equations
583
Contents xxi
17A
Historical
Development
of ¿ -Matrix Theory
587
17B Scattering Processes in Quantum Mechanics
590
17C n-particle Phase Space
595
Problems gOi
18
Exact ¿-Matrices
605
18.1
Yang-Lee and Bullogh-Dodd Models
605
18.2
Ф1)3
Integrable
Deformation of the
Conformai
Minimal Models
A^2,2n+3
608
18.3
Multiple Poles
611
18.4
¿ -Matrices of the Ising Model
612
18.5
The Tricritical Ising Model at
Τ φ
Тс
619
18.6
Thermal Deformation of the Three-state Potts Model
623
18.7
Models with Internal O(n)
Invariance
626
18.8
¿-Matrix of the Sine-Gordon Model
631
18.9
¿-Matrices for
Ф1.3.
Фі,2. Фг.і
Deformation of Minimal Models
635
Problems
651
19
Thermodynamical Bethe
Ansatz 655
19.1
Introduction
655
19.2 Casimir
Energy
655
19.3
Bethe Relativistic Wave Function
658
19.4
Derivation of Thermodynamics
660
19.5
The Meaning of the Pseudo-energy
665
19.6
Infrared and Ultraviolet Limits
668
19.7
The Coefficient of the Bulk Energy
671
19.8
The General Form of the TBA Equations
672
19.9
The Exact Relation A(m)
675
19.10
Examples
677
19.11
Thermodynamics of the Free Field Theories
680
19.12
L-channel Quantization
682
Problems
688
20
Form Factors and Correlation Functions
689
20.1
General Properties of the Form Factors
690
20.2
Watson s Equations
692
20.3
Recursive Equations
695
20.4
The Operator Space
697
20.5
Correlation Functions
697
20.6
Form Factors of the Stress-Energy Tensor
701
20.7
Vacuum Expectation Values
703
20.8
Ultraviolet Limit
706
20.9
The Ising Model at
Τ φ
Тс
709
20.10Form Factors of the Sinh-Gordon Model
714
20.11
The Ising Model in a Magnetic Field
720
Problems
725
xxii Contents
21
Non-Integrable
Aspects
728
21.1
Multiple
Deformations of the
Conformai
Field Theories
728
21.2
Form Factor Perturbation Theory
730
21.3
First-order Perturbation Theory
734
21.4
Non-locality and Confinement
738
21.5
The Scaling Region of the Ising Model
739
Problems
745
Index
747
|
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| discipline | Physik Wirtschaftswissenschaften |
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| id | DE-604.BV035663407 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:42:46Z |
| institution | BVB |
| isbn | 9780199547586 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017717796 |
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| physical | XXII, 755 S. Ill., graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
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| publisher | Oxford Univ. Press |
| record_format | marc |
| series2 | Oxford graduate texts |
| spelling | Mussardo, Giuseppe Verfasser (DE-588)140219064 aut Statistical field theory an introduction to exactly solved models in statistical physics Giuseppe Mussardo 1. publ. Oxford [u.a.] Oxford Univ. Press 2010 XXII, 755 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford graduate texts Hier auch später erschienene, unveränderte Nachdrucke Field theory (Physics) / Statistical methods Field theory (Physics) Statistical methods 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 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017717796&sequence=000002&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 Field theory (Physics) / Statistical methods Field theory (Physics) Statistical methods Quantenfeldtheorie (DE-588)4047984-5 gnd Statistische Mechanik (DE-588)4056999-8 gnd |
| subject_GND | (DE-588)4047984-5 (DE-588)4056999-8 |
| 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 |
| title_fullStr | Statistical field theory an introduction to exactly solved models in statistical physics Giuseppe Mussardo |
| title_full_unstemmed | Statistical field theory an introduction to exactly solved models in statistical physics Giuseppe Mussardo |
| 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 |
| topic | Field theory (Physics) / Statistical methods Field theory (Physics) Statistical methods Quantenfeldtheorie (DE-588)4047984-5 gnd Statistische Mechanik (DE-588)4056999-8 gnd |
| topic_facet | Field theory (Physics) / Statistical methods Field theory (Physics) Statistical methods Quantenfeldtheorie Statistische Mechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017717796&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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