A modern approach to critical phenomena:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2007
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XI, 210 S. graph. Darst. |
| ISBN: | 9780521854528 0521854520 |
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| 245 | 1 | 0 | |a A modern approach to critical phenomena |c Igor Herbut |
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| adam_text | Contents
Preface
page
ix
1
Introduction
1
1.1
Phase transitions and order parameters
1
1.2
Models: Ising, XY,
Heisenberg 3
1.3
Universality and critical exponents
10
1.4
Scaling of free energy
12
1.5
Correlations and hyperscaling
19
2
Ginzburg-Landau-Wilson theory
23
2.1
Partition function for interacting bosons
23
2.2
Bose-Einstein condensation
27
2.3
Hartree
approximation
30
2.4
Landau s mean-field theory
34
2.5
Upper critical dimension
40
3
Renormalization group
43
3.1
Idea
43
3.2
Momentum-shell transformation
46
3.3
e-expansion
53
3.4
Dangerously irrelevant coupling
58
3.5
Corrections to scaling
59
3.6
Field-theoretic perspective
61
3.7
Computation of anomalous dimension
65
3.8
Summary
69
vu
viii Contents
4
Superconducting
transition
77
4.1
Meissner effect
77
4.2
Fluctuation-induced first-order transition
81
4.3
Type-II superconductors near four dimensions
85
4.4
Anomalous dimension for the gauge field
92
4.5
Width of the critical region
93
5
Near lower critical dimension
97
5.1 Goldstone
modes
97
5.2
Mermin-Wagner-Hohenberg theorem
99
5.3
Non-linear
σ
-model
102
5.4
Low-temperature expansion
104
5.5
Discussion
106
6
Kosterlitz-Thouless transition
115
6.1
Vortices and spin waves
115
6.2
Mean-field theory
118
6.3
Duality and the sine-Gordon theory
123
6.4
Renormalization of the sine-Gordon model
131
6.5
Universal jump of superfluid density
138
6.6 Heisenberg
model
140
7
Duality in higher dimensions
147
7.1
Frozen lattice superconductor
147
7.2
Confinement of magnetic
monopoles
152
7.3
Magnetic field correlations
154
7.4
Compact electrodynamics
156
8
Quantum phase transitions
165
8.1
Dynamical critical exponent
165
8.2
Quantum critical point in
Ф4
-theory
168
8.3
Bose-Hubbard model
174
8.4
Quantum fluctuations and the superfluid density
181
8.5
Universal conductivity in two dimensions
185
Appendix A Hubbard-Stratonovich transformation
195
Appendix
В
Linked-cluster theorem
197
Appendix
С
Gauge fixing for long-range order
199
Select bibliography
203
Index
209
The study of critical phenomena is one of the most exciting areas of modern physics. This book
provides a thorough but economic introduction into the principles and techniques of the theory
of critical phenomena and the renormalization group, from the perspective of modern
condensed matter physics. Assuming basic knowledge of quantum and statistical mechanics,
the book discusses phase transitions in magnets, superfluids, superconductors, and gauge field
theories. Particular attention is given to modern topics such as gauge field fluctuations in
superconductors, the Kosterl itz
—
Thou less transition, duality transformations, and quantum
phase transitions, all of which are at the forefront of today s physics research.
A Modern Approach to critical Phenomena contains numerous problems of varying degrees of
difficulty, with solutions. These problems provide readers with a wealth of material to test their
understanding of the subject. It is ideal for graduate students and more experienced researchers
in the fields of condensed matter physics, statistical physics and many-body physics.
IGOR HERBUT is Professor of Physics at Simon
Fraser
University in Bumaby, British Columbia.
He has held visiting appointments atthe Max Planck institute, the Kavli Institute for Theoretical
Physics, and the Tokyo institute of Technology. Professor Herbut has authored a number of
research papers on quantum phase transitions, disordered systems, gauge field theories, and
high-temperature superconductivity.
|
| adam_txt |
Contents
Preface
page
ix
1
Introduction
1
1.1
Phase transitions and order parameters
1
1.2
Models: Ising, XY,
Heisenberg 3
1.3
Universality and critical exponents
10
1.4
Scaling of free energy
12
1.5
Correlations and hyperscaling
19
2
Ginzburg-Landau-Wilson theory
23
2.1
Partition function for interacting bosons
23
2.2
Bose-Einstein condensation
27
2.3
Hartree
approximation
30
2.4
Landau's mean-field theory
34
2.5
Upper critical dimension
40
3
Renormalization group
43
3.1
Idea
43
3.2
Momentum-shell transformation
46
3.3
e-expansion
53
3.4
Dangerously irrelevant coupling
58
3.5
Corrections to scaling
59
3.6
Field-theoretic perspective
61
3.7
Computation of anomalous dimension
65
3.8
Summary
69
vu
viii Contents
4
Superconducting
transition
77
4.1
Meissner effect
77
4.2
Fluctuation-induced first-order transition
81
4.3
Type-II superconductors near four dimensions
85
4.4
Anomalous dimension for the gauge field
92
4.5
Width of the critical region
93
5
Near lower critical dimension
97
5.1 Goldstone
modes
97
5.2
Mermin-Wagner-Hohenberg theorem
99
5.3
Non-linear
σ
-model
102
5.4
Low-temperature expansion
104
5.5
Discussion
106
6
Kosterlitz-Thouless transition
115
6.1
Vortices and spin waves
115
6.2
Mean-field theory
118
6.3
Duality and the sine-Gordon theory
123
6.4
Renormalization of the sine-Gordon model
131
6.5
Universal jump of superfluid density
138
6.6 Heisenberg
model
140
7
Duality in higher dimensions
147
7.1
Frozen lattice superconductor
147
7.2
Confinement of magnetic
monopoles
152
7.3
Magnetic field correlations
154
7.4
Compact electrodynamics
156
8
Quantum phase transitions
165
8.1
Dynamical critical exponent
165
8.2
Quantum critical point in
Ф4
-theory
168
8.3
Bose-Hubbard model
174
8.4
Quantum fluctuations and the superfluid density
181
8.5
Universal conductivity in two dimensions
185
Appendix A Hubbard-Stratonovich transformation
195
Appendix
В
Linked-cluster theorem
197
Appendix
С
Gauge fixing for long-range order
199
Select bibliography
203
Index
209
The study of critical phenomena is one of the most exciting areas of modern physics. This book
provides a thorough but economic introduction into the principles and techniques of the theory
of critical phenomena and the renormalization group, from the perspective of modern
condensed matter physics. Assuming basic knowledge of quantum and statistical mechanics,
the book discusses phase transitions in magnets, superfluids, superconductors, and gauge field
theories. Particular attention is given to modern topics such as gauge field fluctuations in
superconductors, the Kosterl itz
—
Thou less transition, duality transformations, and quantum
phase transitions, all of which are at the forefront of today's physics research.
A Modern Approach to critical Phenomena contains numerous problems of varying degrees of
difficulty, with solutions. These problems provide readers with a wealth of material to test their
understanding of the subject. It is ideal for graduate students and more experienced researchers
in the fields of condensed matter physics, statistical physics and many-body physics.
IGOR HERBUT is Professor of Physics at Simon
Fraser
University in Bumaby, British Columbia.
He has held visiting appointments atthe Max Planck institute, the Kavli Institute for Theoretical
Physics, and the Tokyo institute of Technology. Professor Herbut has authored a number of
research papers on quantum phase transitions, disordered systems, gauge field theories, and
high-temperature superconductivity. |
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| index_date | 2024-07-02T16:39:59Z |
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| spelling | Herbut, Igor Verfasser aut A modern approach to critical phenomena Igor Herbut 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2007 XI, 210 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Groupe de renormalisation Groupe de renormalisation ram Phénomène critique (Physique) Phénomènes critiques (physique) ram Critical phenomena (Physics) Renormalization group Kritisches Phänomen (DE-588)4165788-3 gnd rswk-swf Phasenumwandlung (DE-588)4132140-6 gnd rswk-swf Phasenumwandlung (DE-588)4132140-6 s DE-604 Kritisches Phänomen (DE-588)4165788-3 s Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015463222&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015463222&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Herbut, Igor A modern approach to critical phenomena Groupe de renormalisation Groupe de renormalisation ram Phénomène critique (Physique) Phénomènes critiques (physique) ram Critical phenomena (Physics) Renormalization group Kritisches Phänomen (DE-588)4165788-3 gnd Phasenumwandlung (DE-588)4132140-6 gnd |
| subject_GND | (DE-588)4165788-3 (DE-588)4132140-6 |
| title | A modern approach to critical phenomena |
| title_auth | A modern approach to critical phenomena |
| title_exact_search | A modern approach to critical phenomena |
| title_exact_search_txtP | A modern approach to critical phenomena |
| title_full | A modern approach to critical phenomena Igor Herbut |
| title_fullStr | A modern approach to critical phenomena Igor Herbut |
| title_full_unstemmed | A modern approach to critical phenomena Igor Herbut |
| title_short | A modern approach to critical phenomena |
| title_sort | a modern approach to critical phenomena |
| topic | Groupe de renormalisation Groupe de renormalisation ram Phénomène critique (Physique) Phénomènes critiques (physique) ram Critical phenomena (Physics) Renormalization group Kritisches Phänomen (DE-588)4165788-3 gnd Phasenumwandlung (DE-588)4132140-6 gnd |
| topic_facet | Groupe de renormalisation Phénomène critique (Physique) Phénomènes critiques (physique) Critical phenomena (Physics) Renormalization group Kritisches Phänomen Phasenumwandlung |
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