Scaling and renormalization in statistical physics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2003
|
| Ausgabe: | Repr. with corr., transferred to digital print. |
| Schriftenreihe: | Cambridge lecture notes in physics
5 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 238 S. graph. Darst. |
| ISBN: | 0521499593 9780521499590 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804135072552452096 |
|---|---|
| adam_text | Contents
Preface
page
xiii
1
Phase transitions in simple systems
1
1.1
Phase diagrams
5
1.2
Simple models
10
Exercises
14
2
Mean field theory
16
2.1
The mean field free energy
16
2.2
Critical exponents
20
2.3
Mean field theory for the correlation function
22
2.4
Corrections to mean field theory
24
Exercises
26
3
The renormalization group idea
28
3.1
Block spin transformations
30
3.2
One-dimensional Ising model
34
3.3
General theory
40
3.4
Scaling behaviour of the free energy
43
3.5
Critical exponents
45
3.6
Irrelevant eigenvalues
48
3.7
Scaling for the correlation functions
49
3.8
Scaling operators and scaling dimensions
52
3.9
Critical amplitudes
55
Exercises
59
4
Phase diagrams and fixed points
61
4.1
Ising model with vacancies
61
4.2
Cross-over behaviour
67
4.3
Cross-over to long range behaviour
71
4.4
Finite-size scaling
72
4.5
Quantum critical behaviour
76
ix
Contents
Exercises
«I
5
The perturbative renormalization
group
83
5.1
The operator product expansion
84
5.2
The perturbative renormalization group
86
5.3
The Ising model near four dimensions
90
5.4
The Gaussian fixed point
92
5.5
The Wilson-Fisher fixed point
94
5.6
Logarithmic corrections in
d
= 4
103
5.7
The 0(n) model near four dimensions
104
5.8
Cubic symmetry breaking
107
Exercises
109
6
Low dimensional systems
111
6.1
The lower critical dimension
111
6.2
The two-dimensional XY model
113
6.3
The solid-on-solid model
117
6.4
Renormalization group analysis
120
6.5
The 0(n) model in
2 +
e
dimensions
127
Exercises
131
7
Surface critical behaviour
133
7.1
Mean field theory
134
7.2
The extraordinary and special transitions
136
7.3
Renormalization group approach
138
Exercises
144
б
Random systems
145
8.1
Quenched and annealed disorder
145
8.2
The Harris criterion
148
8.3
Perturbative approach to the random fixed point
150
8.4
Percolation
153
8.5
Random fields
161
Exercises
167
9
Polymer statistics
169
9.1
Random walk model
169
9.2
The Edwards model and the
Flory
formula
170
9.3
Mapping to the O(n) model
172
9.4
Finite concentration
177
9.5
Other applications
178
Contents xi
Exercises
181
10
Critical dynamics
183
10.1
Continuum models
186
10.2
Discrete models
189
10.3
Dynamic scaling
192
10.4
Response functional formalism
193
10.5
Other dynamic universality classes
196
10.6
Directed percolation
200
Exercises
204
11
Conformai
symmetry
206
11.1
Conformai
transformations
209
11.2
Simple consequences of
conformai
symmetry
211
11.3
The stress tensor
215
11.4
Further developments
222
11.5
The c-theorem
223
Exercises
225
Appendix: Gaussian integration
227
Selected bibliography
229
Index
234
|
| adam_txt |
Contents
Preface
page
xiii
1
Phase transitions in simple systems
1
1.1
Phase diagrams
5
1.2
Simple models
10
Exercises
14
2
Mean field theory
16
2.1
The mean field free energy
16
2.2
Critical exponents
20
2.3
Mean field theory for the correlation function
22
2.4
Corrections to mean field theory
24
Exercises
26
3
The renormalization group idea
28
3.1
Block spin transformations
30
3.2
One-dimensional Ising model
34
3.3
General theory
40
3.4
Scaling behaviour of the free energy
43
3.5
Critical exponents
45
3.6
Irrelevant eigenvalues
48
3.7
Scaling for the correlation functions
49
3.8
Scaling operators and scaling dimensions
52
3.9
Critical amplitudes
55
Exercises
59
4
Phase diagrams and fixed points
61
4.1
Ising model with vacancies
61
4.2
Cross-over behaviour
67
4.3
Cross-over to long range behaviour
71
4.4
Finite-size scaling
72
4.5
Quantum critical behaviour
76
ix
Contents
Exercises
«I
5
The perturbative renormalization
group
83
5.1
The operator product expansion
84
5.2
The perturbative renormalization group
86
5.3
The Ising model near four dimensions
90
5.4
The Gaussian fixed point
92
5.5
The Wilson-Fisher fixed point
94
5.6
Logarithmic corrections in
d
= 4
103
5.7
The 0(n) model near four dimensions
104
5.8
Cubic symmetry breaking
107
Exercises
109
6
Low dimensional systems
111
6.1
The lower critical dimension
111
6.2
The two-dimensional XY model
113
6.3
The solid-on-solid model
117
6.4
Renormalization group analysis
120
6.5
The 0(n) model in
2 +
e
dimensions
127
Exercises
131
7
Surface critical behaviour
133
7.1
Mean field theory
134
7.2
The extraordinary and special transitions
136
7.3
Renormalization group approach
138
Exercises
144
б
Random systems
145
8.1
Quenched and annealed disorder
145
8.2
The Harris criterion
148
8.3
Perturbative approach to the random fixed point
150
8.4
Percolation
153
8.5
Random fields
161
Exercises
167
9
Polymer statistics
169
9.1
Random walk model
169
9.2
The Edwards model and the
Flory
formula
170
9.3
Mapping to the O(n) model
172
9.4
Finite concentration
177
9.5
Other applications
178
Contents xi
Exercises
181
10
Critical dynamics
183
10.1
Continuum models
186
10.2
Discrete models
189
10.3
Dynamic scaling
192
10.4
Response functional formalism
193
10.5
Other dynamic universality classes
196
10.6
Directed percolation
200
Exercises
204
11
Conformai
symmetry
206
11.1
Conformai
transformations
209
11.2
Simple consequences of
conformai
symmetry
211
11.3
The stress tensor
215
11.4
Further developments
222
11.5
The c-theorem
223
Exercises
225
Appendix: Gaussian integration
227
Selected bibliography
229
Index
234 |
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| discipline | Physik |
| discipline_str_mv | Physik |
| edition | Repr. with corr., transferred to digital print. |
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| spelling | Cardy, John 1947- Verfasser (DE-588)1215790988 aut Scaling and renormalization in statistical physics John Cardy Repr. with corr., transferred to digital print. Cambridge [u.a.] Cambridge Univ. Press 2003 XVII, 238 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge lecture notes in physics 5 Renormierung (DE-588)4128419-7 gnd rswk-swf Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf Renormierungsgruppe (DE-588)4177773-6 gnd rswk-swf Skalierung (DE-588)4055202-0 gnd rswk-swf Statistische Physik (DE-588)4057000-9 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Statistische Physik (DE-588)4057000-9 s Skalierung (DE-588)4055202-0 s 2\p DE-604 Renormierung (DE-588)4128419-7 s 3\p DE-604 Renormierungsgruppe (DE-588)4177773-6 s Statistische Mechanik (DE-588)4056999-8 s 4\p DE-604 Cambridge lecture notes in physics 5 (DE-604)BV009623742 5 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014605254&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cardy, John 1947- Scaling and renormalization in statistical physics Cambridge lecture notes in physics Renormierung (DE-588)4128419-7 gnd Statistische Mechanik (DE-588)4056999-8 gnd Renormierungsgruppe (DE-588)4177773-6 gnd Skalierung (DE-588)4055202-0 gnd Statistische Physik (DE-588)4057000-9 gnd |
| subject_GND | (DE-588)4128419-7 (DE-588)4056999-8 (DE-588)4177773-6 (DE-588)4055202-0 (DE-588)4057000-9 (DE-588)4123623-3 |
| title | Scaling and renormalization in statistical physics |
| title_auth | Scaling and renormalization in statistical physics |
| title_exact_search | Scaling and renormalization in statistical physics |
| title_exact_search_txtP | Scaling and renormalization in statistical physics |
| title_full | Scaling and renormalization in statistical physics John Cardy |
| title_fullStr | Scaling and renormalization in statistical physics John Cardy |
| title_full_unstemmed | Scaling and renormalization in statistical physics John Cardy |
| title_short | Scaling and renormalization in statistical physics |
| title_sort | scaling and renormalization in statistical physics |
| topic | Renormierung (DE-588)4128419-7 gnd Statistische Mechanik (DE-588)4056999-8 gnd Renormierungsgruppe (DE-588)4177773-6 gnd Skalierung (DE-588)4055202-0 gnd Statistische Physik (DE-588)4057000-9 gnd |
| topic_facet | Renormierung Statistische Mechanik Renormierungsgruppe Skalierung Statistische Physik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014605254&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009623742 |
| work_keys_str_mv | AT cardyjohn scalingandrenormalizationinstatisticalphysics |