Statistical physics of fields:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2007
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | X, 359 S. graph. Darst. |
| ISBN: | 9780521873413 |
Internformat
MARC
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| 100 | 1 | |a Kardar, Mehran |e Verfasser |0 (DE-588)13350428X |4 aut | |
| 245 | 1 | 0 | |a Statistical physics of fields |c Mehran Kardar |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2007 | |
| 300 | |a X, 359 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Field theory (Physics) | |
| 650 | 4 | |a Statistical physics | |
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Datensatz im Suchindex
| _version_ | 1804136596491993088 |
|---|---|
| adam_text | Contents
Preface
page
ix
1
Collective behavior, from particles to fields
1
1.1
Introduction
1
1.2
Phonons and elasticity
3
1.3
Phase transitions
9
1.4
Critical behavior
11
Problems
14
2
Statistical fields
19
2.1
Introduction
19
2.2
The Landau-Ginzburg Hamiltonian
21
2.3
Saddle point approximation, and mean-field theory
24
2.4
Continuous symmetry breaking and
Goldstone
modes
29
2.5
Discrete symmetry breaking and domain walls
31
Problems
32
3
Fluctuations
35
3.1
Scattering and fluctuations
35
3.2
Correlation functions and susceptibilities
37
3.3
Lower critical dimension
39
3.4
Comparison to experiments
42
3.5
Gaussian integrals
43
3.6
Fluctuation corrections to the saddle point
45
3.7
The Ginzburg criterion
47
Problems
48
4
The scaling hypothesis
54
4.1
The homogeneity assumption
54
4.2
Divergence of the correlation length
57
4.3
Critical correlation functions and self-similarity
59
4.4
The renormalization group (conceptual)
60
vi
Contents
4.5
The renormalization group (formal)
63
4.6
The Gaussian model (direct solution)
66
4.7
The Gaussian model (renormalization group)
68
Problems
70
5
Perturbative renormalization group
73
5.1
Expectation values in the Gaussian model
73
5.2
Expectation values in perturbation theory
74
5.3
Diagrammatic representation of perturbation theory
76
5.4
Susceptibility
78
5.5
Perturbative RG (first order)
80
5.6
Perturbative RG (second order)
84
5.7
The e-expansion
87
5.8
Irrelevance of other interactions
90
5.9
Comments on the e-expansion
92
Problems
93
6
Lattice systems
98
6.1
Models and methods
98
6.2
Transfer matrices
101
6.3
Position space RG in one dimension
104
6.4
The Niemeijer-van
Leeuwen
cumulant
approximation
108
6.5
The Migdal-Kadanoff bond moving approximation
112
6.6
Monte Carlo simulations
114
Problems
117
7
Series expansions
123
7.1
Low-temperature expansions
123
7.2
High-temperature expansions
125
7.3
Exact solution of the one-dimensional Ising model
127
7.4
Self-duality in the two-dimensional Ising model
128
7.5
Dual of the three-dimensional Ising model
130
7.6
Summing over phantom loops
133
7.7
Exact free energy of the square lattice Ising model
140
7.8
Critical behavior of the two-dimensional Ising model
146
Problems
148
8
Beyond spin waves
156
8.1
The nonlinear
σ
model
156
8.2
Topological defects in the XY model
162
8.3
Renormalization group for the Coulomb gas
168
8.4
Two-dimensional solids
174
Contents
vii
8.5
Two-dimensional melting
177
Problems
181
9
Dissipative dynamics
188
9.1
Brownian motion of a particle
188
9.2
Equilibrium dynamics of a field
192
9.3
Dynamics of a conserved field
194
9.4
Generic scale
invariance
in equilibrium systems
196
9.5
Non-equilibrium dynamics of open systems
200
9.6
Dynamics of a growing surface
204
10
Directed paths in random media
209
10.1
Introduction
209
10.2
High-
Γ
expansions for the random-bond Ising model
210
10.3
The one-dimensional chain
213
10.4
Directed paths and the transfer matrix
216
10.5
Moments of the correlation function
221
10.6
The probability distribution in two dimensions
226
10.7
Higher dimensions
229
10.8
Random signs
233
10.9
Other realizations of DPRM
237
10.10
Quantum interference of strongly localized electrons
241
10.11
The locator expansion and forward scattering paths
244
10.12
Magnetic field response
247
10.13
Unitary propagation
252
10.14
Unitary averages
255
Solutions to selected problems
260
Chapter
1 260
Chapter
2 268
Chapter
3 278
Chapter
4 292
Chapter
5 298
Chapter
6 317
Chapter
7 324
Chapter
8 343
Index
357
|
| adam_txt |
Contents
Preface
page
ix
1
Collective behavior, from particles to fields
1
1.1
Introduction
1
1.2
Phonons and elasticity
3
1.3
Phase transitions
9
1.4
Critical behavior
11
Problems
14
2
Statistical fields
19
2.1
Introduction
19
2.2
The Landau-Ginzburg Hamiltonian
21
2.3
Saddle point approximation, and mean-field theory
24
2.4
Continuous symmetry breaking and
Goldstone
modes
29
2.5
Discrete symmetry breaking and domain walls
31
Problems
32
3
Fluctuations
35
3.1
Scattering and fluctuations
35
3.2
Correlation functions and susceptibilities
37
3.3
Lower critical dimension
39
3.4
Comparison to experiments
42
3.5
Gaussian integrals
43
3.6
Fluctuation corrections to the saddle point
45
3.7
The Ginzburg criterion
47
Problems
48
4
The scaling hypothesis
54
4.1
The homogeneity assumption
54
4.2
Divergence of the correlation length
57
4.3
Critical correlation functions and self-similarity
59
4.4
The renormalization group (conceptual)
60
vi
Contents
4.5
The renormalization group (formal)
63
4.6
The Gaussian model (direct solution)
66
4.7
The Gaussian model (renormalization group)
68
Problems
70
5
Perturbative renormalization group
73
5.1
Expectation values in the Gaussian model
73
5.2
Expectation values in perturbation theory
74
5.3
Diagrammatic representation of perturbation theory
76
5.4
Susceptibility
78
5.5
Perturbative RG (first order)
80
5.6
Perturbative RG (second order)
84
5.7
The e-expansion
87
5.8
Irrelevance of other interactions
90
5.9
Comments on the e-expansion
92
Problems
93
6
Lattice systems
98
6.1
Models and methods
98
6.2
Transfer matrices
101
6.3
Position space RG in one dimension
104
6.4
The Niemeijer-van
Leeuwen
cumulant
approximation
108
6.5
The Migdal-Kadanoff bond moving approximation
112
6.6
Monte Carlo simulations
114
Problems
117
7
Series expansions
123
7.1
Low-temperature expansions
123
7.2
High-temperature expansions
125
7.3
Exact solution of the one-dimensional Ising model
127
7.4
Self-duality in the two-dimensional Ising model
128
7.5
Dual of the three-dimensional Ising model
130
7.6
Summing over phantom loops
133
7.7
Exact free energy of the square lattice Ising model
140
7.8
Critical behavior of the two-dimensional Ising model
146
Problems
148
8
Beyond spin waves
156
8.1
The nonlinear
σ
model
156
8.2
Topological defects in the XY model
162
8.3
Renormalization group for the Coulomb gas
168
8.4
Two-dimensional solids
174
Contents
vii
8.5
Two-dimensional melting
177
Problems
181
9
Dissipative dynamics
188
9.1
Brownian motion of a particle
188
9.2
Equilibrium dynamics of a field
192
9.3
Dynamics of a conserved field
194
9.4
Generic scale
invariance
in equilibrium systems
196
9.5
Non-equilibrium dynamics of open systems
200
9.6
Dynamics of a growing surface
204
10
Directed paths in random media
209
10.1
Introduction
209
10.2
High-
Γ
expansions for the random-bond Ising model
210
10.3
The one-dimensional chain
213
10.4
Directed paths and the transfer matrix
216
10.5
Moments of the correlation function
221
10.6
The probability distribution in two dimensions
226
10.7
Higher dimensions
229
10.8
Random signs
233
10.9
Other realizations of DPRM
237
10.10
Quantum interference of strongly localized electrons
241
10.11
The locator expansion and forward scattering paths
244
10.12
Magnetic field response
247
10.13
Unitary propagation
252
10.14
Unitary averages
255
Solutions to selected problems
260
Chapter
1 260
Chapter
2 268
Chapter
3 278
Chapter
4 292
Chapter
5 298
Chapter
6 317
Chapter
7 324
Chapter
8 343
Index
357 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T17:54:31Z |
| indexdate | 2024-07-09T20:58:55Z |
| institution | BVB |
| isbn | 9780521873413 |
| language | English |
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| physical | X, 359 S. graph. Darst. |
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| spelling | Kardar, Mehran Verfasser (DE-588)13350428X aut Statistical physics of fields Mehran Kardar 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2007 X, 359 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Field theory (Physics) Statistical physics Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content (DE-588)4123623-3 Lehrbuch gnd-content Statistische Mechanik (DE-588)4056999-8 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015705523&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kardar, Mehran Statistical physics of fields Field theory (Physics) Statistical physics Statistische Mechanik (DE-588)4056999-8 gnd |
| subject_GND | (DE-588)4056999-8 (DE-588)4143389-0 (DE-588)4123623-3 |
| title | Statistical physics of fields |
| title_auth | Statistical physics of fields |
| title_exact_search | Statistical physics of fields |
| title_exact_search_txtP | Statistical physics of fields |
| title_full | Statistical physics of fields Mehran Kardar |
| title_fullStr | Statistical physics of fields Mehran Kardar |
| title_full_unstemmed | Statistical physics of fields Mehran Kardar |
| title_short | Statistical physics of fields |
| title_sort | statistical physics of fields |
| topic | Field theory (Physics) Statistical physics Statistische Mechanik (DE-588)4056999-8 gnd |
| topic_facet | Field theory (Physics) Statistical physics Statistische Mechanik Aufgabensammlung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015705523&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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