Modern Approach Critical Phenomena

By: Igor Herbut

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Hardcover | 4 January 2007

At a Glance

Hardcover
224 Pages

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24.41 x 16.99 x 1.42

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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 Kosterlitz-Thouless transition, duality transformations, and quantum phase transitions - all of which are at the forefront of today's physics research. This book 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.

Industry Reviews

'This relatively short and extremely well written book is what i would recommend to every graduate student in condensed matter physics as compulsory reading. ...I am sure the students will appreciate its manageable size and conciseness, its crisp argumentation as well as its elegant and not overwhelming mathematical proofs.' Journal of Statistical Physics

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You Can Find This Book In

Non-Fiction Science Physics Statistical Physics Atomic & Molecular Physics

Preface	p. ix
Introduction	p. 1
Phase transitions and order parameters	p. 1
Models: Ising, XY, Heisenberg	p. 3
Universality and critical exponents	p. 10
Scaling of free energy	p. 12
Correlations and hyperscaling	p. 19
Ginzburg-Landau-Wilson theory	p. 23
Partition function for interacting bosons	p. 23
Bose-Einstein condensation	p. 27
Hartree approximation	p. 30
Landau's mean-field theory	p. 34
Upper critical dimension	p. 40
Renormalization group	p. 43
Idea	p. 43
Momentum-shell transformation	p. 46
[epsi]-expansion	p. 53
Dangerously irrelevant coupling	p. 58
Corrections to scaling	p. 59
Field-theoretic perspective	p. 61
Computation of anomalous dimension	p. 65
Summary	p. 69
Superconducting transition	p. 77
Meissner effect	p. 77
Fluctuation-induced first-order transition	p. 81
Type-II superconductors near four dimensions	p. 85
Anomalous dimension for the gauge field	p. 92
Width of the critical region	p. 93
Near lower critical dimension	p. 97
Goldstone modes	p. 97
Mermin-Wagner-Hohenberg theorem	p. 99
Non-linear [sigma]-model	p. 102
Low-temperature expansion	p. 104
Discussion	p. 106
Kosterlitz-Thouless transition	p. 115
Vortices and spin waves	p. 115
Mean-field theory	p. 118
Duality and the sine-Gordon theory	p. 123
Renormalization of the sine-Gordon model	p. 131
Universal jump of superfluid density	p. 138
Heisenberg model	p. 140
Duality in higher dimensions	p. 147
Frozen lattice superconductor	p. 147
Confinement of magnetic monopoles	p. 152
Magnetic field correlations	p. 154
Compact electrodynamics	p. 156
Quantum phase transitions	p. 165
Dynamical critical exponent	p. 165
Quantum critical point in [Phi superscript 4]-theory	p. 168
Bose-Hubbard model	p. 174
Quantum fluctuations and the superfluid density	p. 181
Universal conductivity in two dimensions	p. 185
Hubbard-Stratonovich transformation	p. 195
Linked-cluster theorem	p. 197
Gauge fixing for long-range order	p. 199
Select bibliography	p. 203
Index	p. 209
Table of Contents provided by Ingram. All Rights Reserved.

Modern Approach Critical Phenomena

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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