Introduction to statistical field theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2010
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 166 S. graph. Darst. |
| ISBN: | 9780521193030 |
Internformat
MARC
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| 100 | 1 | |a Brézin, Edouard |d 1938- |e Verfasser |0 (DE-588)142077704 |4 aut | |
| 245 | 1 | 0 | |a Introduction to statistical field theory |c Edouard Brézin |
| 246 | 1 | 3 | |a Statistical field theory |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2010 | |
| 300 | |a X, 166 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Phase transformations (Statistical physics) | |
| 650 | 4 | |a Field theory (Physics) | |
| 650 | 4 | |a Statistical mechanics | |
| 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 |
| 689 | 0 | 0 | |a Statistische Mechanik |0 (DE-588)4056999-8 |D s |
| 689 | 0 | 1 | |a Quantenfeldtheorie |0 (DE-588)4047984-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020481330&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-020481330 | ||
Datensatz im Suchindex
| _version_ | 1804143135832408064 |
|---|---|
| adam_text | Contents
Preface
page
ix
A few well-known basic results
1
1.1
The Boltzmann law
1
1.1.1
The classical canonical ensemble
1
1.1.2
The quantum canonical ensemble
2
1.1.3
The grand canonical ensemble
3
1.2
Thermodynamics from statistical physics
3
1.2.1
The thermodynamic limit
3
1.3
Gaussian integrals and Wick s theorem
4
1.4
Functional derivatives
6
1.5
¿/-dimensional integrals
6
Additional references
8
Introduction: order parameters, broken symmetries
9
2.1
Can statistical mechanics be used to describe phase
transitions?
9
2.2
The order-disorder competition
10
2.3
Order parameter, symmetry and broken symmetry
12
2.4
More general symmetries
16
2.5
Characterization of a phase transition through
correlations
18
2.6
Phase coexistence, critical points, critical exponents
19
Examples of physical situations modelled by the Ising model
22
3.1
Heisenberg s exchange forces
22
3.2 Heisenberg
and Ising Hamiltonians
24
3.3
Lattice gas
26
3.4
More examples
28
3.5
A first connection with field theory
29
vi
Contents
4
A
few results for the Ising model
32
4.1
One-dimensional Ising model: transfer matrix
32
4.2
One-dimensional Ising model: correlation functions
35
4.3
Absence of phase transition in one dimension
37
4.4
A glance at the two-dimensional Ising model
38
4.5
Proof of broken symmetry in two dimensions (and more)
38
4.6
Correlation inequalities
42
4.7
Lower critical dimension: heuristic approach
44
4.8
Digression: Feynman path integrals, the transfer matrix and
the
Schrödinger
equation
47
5
High-temperature and low-temperature expansions
52
5.1
High-temperature expansion for the Ising model
52
5.1.1
Continuous symmetry
55
5.2
Low-temperature expansion
56
5.2.1
Kramers-Wannier duality
57
5.3
Low-temperature expansion for a continuous symmetry group
58
6
Some geometric problems related to phase transitions
60
6.1
Polymers and self-avoiding walks
60
6.2
Potts model and percolation
64
7
Phenomenological description of critical behaviour
68
7.1
Landau theory
68
7.2
Landau theory near the critical point: homogeneous case
71
7.3
Landau theory and spatial correlations
75
7.4
Transitions without symmetry breaking: the liquid-gas
transition
78
7.5
Thermodynamic meaning of
Γ
{m}
79
7.6
Universality
80
7.7
Scaling laws
82
8
Mean field theory
85
8.1
Weiss molecular field
85
8.2
Mean field theory: the variational method
87
8.3
A simpler alternative approach
92
9
Beyond the mean field theory
95
9.1
The first correction to the mean-field free energy
95
9.2
Physical consequences
97
10
Introduction to the renormalization group
100
10.1
Renormalized theories and critical points
101
10.2
Kadanoff block spins
101
10.3
Examples of real space renormalization groups: decimation
103
10.4
Structure of the renormalization group equations
109
Contents
vii
11 Renormalization
group for the
φ4
theory
113
11.1
Renormalization group
...
without renormalization
114
11.2
Study of the renormalization group flow in dimension four
116
11.3
Critical behaviour of the susceptibility in dimension four
118
11.4
Multi-component order parameters
120
11.5 Epsilon
expansion
122
11.6
An exercise on the renormalization group: the cubic fixed
point
125
12
Renormalized theory
128
12.1
The meaning of renormalizability
128
12.2
Renormalization of the massless theory
132
12.3
The renormalized critical free energy (at one-loop order)
134
12.4
Away from Tc
136
13 Goldstone
modes
138
13.1
Broken symmetries and massless modes
138
13.2
Linear and non-linear
О (и)
sigma
models
142
13.3
Regularization and renormalization of the O(n) non-linear
sigma
model in two dimensions
144
13.3.1
Regularization
144
13.3.2
Perturbation expansion and renormalization
148
13.4
Renormalization group equations for the O(n) non-linear
sigma
model and the (d
— 2)
expansion
150
13.4.1
Integration of RG equations and scaling
151
13.5
Extensions to other non-linear
sigma
models
153
14
Large
л
156
14.1
The linear O(n) model
156
14.2
О (и)
sigma
model
161
Index
165
|
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| author_facet | Brézin, Edouard 1938- |
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| discipline | Physik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV036559963 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:42:51Z |
| institution | BVB |
| isbn | 9780521193030 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020481330 |
| oclc_num | 705661591 |
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| owner_facet | DE-20 DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-11 DE-29T DE-91G DE-BY-TUM DE-703 |
| physical | X, 166 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Cambridge Univ. Press |
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| spelling | Brézin, Edouard 1938- Verfasser (DE-588)142077704 aut Introduction to statistical field theory Edouard Brézin Statistical field theory 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2010 X, 166 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Phase transformations (Statistical physics) Field theory (Physics) Statistical mechanics 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 Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020481330&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brézin, Edouard 1938- Introduction to statistical field theory Phase transformations (Statistical physics) Field theory (Physics) Statistical mechanics Quantenfeldtheorie (DE-588)4047984-5 gnd Statistische Mechanik (DE-588)4056999-8 gnd |
| subject_GND | (DE-588)4047984-5 (DE-588)4056999-8 |
| title | Introduction to statistical field theory |
| title_alt | Statistical field theory |
| title_auth | Introduction to statistical field theory |
| title_exact_search | Introduction to statistical field theory |
| title_full | Introduction to statistical field theory Edouard Brézin |
| title_fullStr | Introduction to statistical field theory Edouard Brézin |
| title_full_unstemmed | Introduction to statistical field theory Edouard Brézin |
| title_short | Introduction to statistical field theory |
| title_sort | introduction to statistical field theory |
| topic | Phase transformations (Statistical physics) Field theory (Physics) Statistical mechanics Quantenfeldtheorie (DE-588)4047984-5 gnd Statistische Mechanik (DE-588)4056999-8 gnd |
| topic_facet | Phase transformations (Statistical physics) Field theory (Physics) Statistical mechanics Quantenfeldtheorie Statistische Mechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020481330&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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