Elements of phase transitions and critical phenomena:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford u.a.
Oxford University Press
2011
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XIII, 358 S. graph. Darst. |
| ISBN: | 9780199577224 9780198754084 |
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| 245 | 1 | 0 | |a Elements of phase transitions and critical phenomena |c Hidetoshi Nishimori ; Gerardo Ortiz |
| 250 | |a 1. publ. | ||
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Record in the Search Index
| _version_ | 1804143683282403328 |
|---|---|
| adam_text | Contents
1 Phase
transitions
and critical phenomena
1
1.1
Phase and phase diagram
1
1.2
Phase transitions
2
1.3
Critical phenomena
5
1.4
Scale transformation and renormalization group
7
1.5
Ising model and related systems
12
2
Mean-field theories
16
2.1
Mean-field approximation
16
2.2
Critical exponents of the mean-field theory
19
2.3
Landau theory
22
2.4
Landau theory of the tricritical point
27
2.5
Infinite-range model
30
2.6
Variational method
32
2.7
Antiferromagnetic Ising model
34
2.8
Bethe approximation
36
2.9
Correlation function
40
2.10
Limit of applicability of the mean-field approximation
44
2.11
Dynamic critical phenomena
46
3
Renormalization group and scaling
52
3.1
Coarse-graining and scale transformations
52
3.2
Parameter space and renormalization group equation
55
3.3
Renormalization group flow near a fixed point and universality
60
3.4
Scaling law and critical exponents
62
3.5
Scaling law for correlation functions and hyperscaling
65
3.6
A simple example: One-dimensional Ising model
67
3.7
Mean-field theory and scaling law
72
3.8
Scaling dimension and scaling law
73
3.9
Scaling and anomalous dimensions
75
3.10
Data analysis by scaling law and finite-size scaling
76
3.11
Crossover phenomena
79
3.12
Dynamic scaling law
81
4
Implementation of the renormalization group
4.1
Real-space renormalization group for arbitrary dimensions
4.2
Momentum-space renormalization group:
e
= 4 —
d
expansion
4.3
Real-space renormalization group for a quantum system
83
83
92
98
xii
Contents
5
Statistical field theory
105
5.1
From bits to fields
105
5.2
Continuum limit and field theory
106
5.3
Hubbard-Stratonovich transformation
109
5.4
Integrating out degrees of freedom: Coarse graining 111
5.5
Phenomenological Landau-Ginzburg approach
113
5.6
Symmetry and its breakdown
116
5.7
Nambu-Goldstone modes
120
5.8
Topological defects
123
6
Conformai
field theory
128
6.1
From scale
invariance
to
conformai
symmetry
128
6.2
Conformai
transformation
129
6.3
Primary and quasi-primary operators
132
6.4
Energy-momentum tensor and the Ward identity
135
6.5
Virasoro algebra
139
6.6
Gaussian theory
140
6.7
Operator formalism
142
6.8
Unitary representation of the Virasoro algebra
147
6.9
Ising model
149
6.10
Finite-size effects
150
7
Kosterlitz—Thouless transition
153
7.1
Peierls argument
153
7.2
Lower critical dimension of the XY model
155
7.3
Mermin-Wagner theorem: Absence of spontaneous magnetization
158
7.4
Kosterlitz-Thouless transition
161
7.5
Interaction energy of vortex pairs
165
7.6
Renormalization group analysis
167
7.7
Lattice gauge theory and Elitzur s theorem
172
8
Random systems
178
8.1
Random fields
178
8.2
Spin glass
187
8.3
Diluted ferromagnet and percolation
193
9
Exact solutions and related topics
204
9.1
One-dimensional Ising model
204
9.2
One-dimensional n-vector model
211
9.3
Spherical model
214
9.4
One-dimensional quantum XY model
219
9.5
Two-dimensional Ising model
224
9.6
Zeros of the partition function
231
10
Duality
235
10.1
Classical duality
235
10.2
High- and low-temperature series expansions
238
Contents xiü
10.3
Duality by Fourier transformation
244
10.4
Quantum duality
253
11
Numerical methods
258
11.1
Master equation
258
11.2
Monte Carlo simulation
261
11.3
Numerical transfer matrix method
264
For further reading
266
Appendix A
268
A.I Saddle-point method
268
A.
2
Expressing the susceptibility in terms of correlation functions
270
A.3 Rushbrooke s inequality
272
A.
4
Cumulants
274
A.
5
Renormalization group equations from the
e
expansion
274
A.
6
Symmetry and Noether s theorem
284
A.
7
Basics of group theory and Lie algebras
290
A.
8
Basics of homotopy theory
293
A.
9
Restrictions on the type of
conformai
mappings
294
A.
10
Properties of the energy-momentum tensor
296
A.
11
Energy-momentum tensor of the Gaussian theory
297
A.
12
Existence of spontaneous magnetization in the two-dimensional
Ising model
298
A.
13
Quantum version of the Mermin-Wagner theorem
301
A.
14
Replica symmetric solution of the SK model
305
A.
15
Integral for the partition function of the n-vector model
309
A.
16
Multiple Gaussian integral and lattice Green function
310
A.
17
Jordan-Wigner transformation
313
A.18 Proof of Theorem
9.1 315
A.
19
Poisson
summation formula
318
A.
20
Sample codes for Monte Carlo simulation of the Ising model
319
Appendix B: Solutions to exercises
324
Index
354
|
| any_adam_object | 1 |
| author | Nishimori, Hidetoshi Ortiz, Gerardo |
| author_GND | (DE-588)143260790 |
| author_facet | Nishimori, Hidetoshi Ortiz, Gerardo |
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| author_sort | Nishimori, Hidetoshi |
| author_variant | h n hn g o go |
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| bvnumber | BV036958951 |
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| callnumber-subject | QC - Physics |
| classification_rvk | UG 3800 |
| ctrlnum | (OCoLC)711801774 (DE-599)BVBBV036958951 |
| dewey-full | 530.4/74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.4/74 |
| dewey-search | 530.4/74 |
| dewey-sort | 3530.4 274 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 1. publ. |
| format | Book |
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| institution | BVB |
| isbn | 9780199577224 9780198754084 |
| language | English |
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| physical | XIII, 358 S. graph. Darst. |
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| publisher | Oxford University Press |
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| spelling | Nishimori, Hidetoshi Verfasser aut Elements of phase transitions and critical phenomena Hidetoshi Nishimori ; Gerardo Ortiz 1. publ. Oxford u.a. Oxford University Press 2011 XIII, 358 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Phase transformations (Statistical physics) Feldtheorie (DE-588)4016698-3 gnd rswk-swf Phasenumwandlung (DE-588)4132140-6 gnd rswk-swf Kritisches Phänomen (DE-588)4165788-3 gnd rswk-swf Phasenumwandlung (DE-588)4132140-6 s Kritisches Phänomen (DE-588)4165788-3 s Feldtheorie (DE-588)4016698-3 s 1\p DE-604 Ortiz, Gerardo Verfasser (DE-588)143260790 aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020873866&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Nishimori, Hidetoshi Ortiz, Gerardo Elements of phase transitions and critical phenomena Phase transformations (Statistical physics) Feldtheorie (DE-588)4016698-3 gnd Phasenumwandlung (DE-588)4132140-6 gnd Kritisches Phänomen (DE-588)4165788-3 gnd |
| subject_GND | (DE-588)4016698-3 (DE-588)4132140-6 (DE-588)4165788-3 |
| title | Elements of phase transitions and critical phenomena |
| title_auth | Elements of phase transitions and critical phenomena |
| title_exact_search | Elements of phase transitions and critical phenomena |
| title_full | Elements of phase transitions and critical phenomena Hidetoshi Nishimori ; Gerardo Ortiz |
| title_fullStr | Elements of phase transitions and critical phenomena Hidetoshi Nishimori ; Gerardo Ortiz |
| title_full_unstemmed | Elements of phase transitions and critical phenomena Hidetoshi Nishimori ; Gerardo Ortiz |
| title_short | Elements of phase transitions and critical phenomena |
| title_sort | elements of phase transitions and critical phenomena |
| topic | Phase transformations (Statistical physics) Feldtheorie (DE-588)4016698-3 gnd Phasenumwandlung (DE-588)4132140-6 gnd Kritisches Phänomen (DE-588)4165788-3 gnd |
| topic_facet | Phase transformations (Statistical physics) Feldtheorie Phasenumwandlung Kritisches Phänomen |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020873866&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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