Statistical Field Theory

From Brownian Motion to Renormalization and Lattice Gauge Theory

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Paperback | 29 July 1991

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Volume 1: From Brownian Motion to Renormalization and Lattice Gauge Theory. Volume 2: Strong Coupling, Monte Carlo Methods, Conformal Field Theory, and Random Systems. This two-volume work provides a comprehensive and timely survey of the application of the methods of quantum field theory to statistical physics, a very active and fruitful area of modern research. The first volume provides a pedagogical introduction to the subject, discussing Brownian motion, its anticommutative counterpart in the guise of Onsager's solution to the two-dimensional Ising model, the mean field or Landau approximation, scaling ideas exemplified by the Kosterlitz-Thouless theory for the XY transition, the continuous renormalization group applied to the standard phi-to the fourth theory (the simplest typical case) and lattice gauge theory as a pathway to the understanding of quark confinement in quantum chromodynamics. The second volume covers more diverse topics, including strong coupling expansions and their analysis, Monte Carlo simulations, two-dimensional conformal field theory, and simple disordered systems. The book concludes with a chapter on random geometry and the Polyakov model of random surfaces which illustrates the relations between string theory and statistical physics. The two volumes that make up this work will be useful to theoretical physicists and applied mathematicians who are interested in the exciting developments which have resulted from the synthesis of field theory and statistical physics.

Industry Reviews

"I strongly recommend these two volumes to anyone from intermediate graduate students to active experienced researchers to aging veterans who need to be reminded of or learn for the first time the broad conceptual framework underlying the many current applications of field theoretic methods." Paul Ginsparg, Foundations of Physics "...an excellent pedagogically oriented introduction to the essential fundamentals of this rapidly expanding field. The level of treatment and clarity make it suitable for use as a primary reference in a graduate course." D. J. Geldart, Physics in Canada

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Non-Fiction Science Physics Statistical Physics

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Non-Fiction Science Physics Statistical Physics

Contents of Volume 2	p. ix
Preface	p. xi
From Brownian motion to Euclidean fields	p. 1
Brownian motion	p. 1
Random walks	p. 1
The sum over paths	p. 9
The dimension two of Brownian curves	p. 12
Euclidean fields	p. 21
Free fields	p. 22
Interacting fields and random walks	p. 25
Self-avoiding walks and the limit n [right arrow] 0	p. 31
Comparison with the high temperature expansion	p. 33
The one-dimensional case	p. 37
Lattices	p. 43
Notes	p. 47
Grassmannian integrals and the two-dimensional Ising model	p. 48
Grassmannian integrals	p. 48
Anticommuting variables	p. 48
Integrals	p. 52
The two-dimensional Ising model	p. 58
Duality	p. 59
Transfer matrix	p. 62
Fermionic representation	p. 63
Free energy	p. 67
Spontaneous magnetization	p. 72
Correlation function in the high temperature phase	p. 78
Surface tension	p. 85
Critical continuous theory	p. 91
Effective action	p. 91
Correlation functions	p. 95
Quadratic differences and Painleve equations	p. 98
Notes	p. 104
Spontaneous symmetry breaking, mean field	p. 107
Mean field approximation	p. 108
Dielectric constant of a polarizable medium	p. 108
Classical spin model with a finite symmetry group	p. 112
Continuous symmetry group	p. 118
The Bethe approximation	p. 121
Critical exponents	p. 125
Lee-Yang zeroes	p. 131
The Lee-Yang theorem	p. 132
The one-dimensional case	p. 135
General properties	p. 136
Zeroes in the temperature plane	p. 139
Large n limit	p. 140
Saddle point method	p. 141
Factorization	p. 145
Coupling to an external field	p. 148
Corrections to mean field	p. 151
Laplace transform	p. 153
Notes	p. 159
Scaling transformations and the XY-model	p. 162
Scaling laws. Real space renormalization	p. 162
Homogeneity and scale invariance	p. 162
Recurrence relations in real space	p. 168
Examples and approximations	p. 176
The XY-model	p. 193
High temperature behaviour	p. 195
Low temperature expansion. Vortices	p. 197
The Villain action	p. 204
Correlations	p. 207
Renormalization flow	p. 213
Two-dimensional systems with continuous symmetry	p. 219
Magnetization inequality	p. 219
Correlation inequality	p. 222
Phenomenological renormalization	p. 224
Notes	p. 230
Continuous field theory and the renormalization group	p. 233
The Lagrangian and dimensional analysis	p. 233
Introduction	p. 233
Generating functionals and dimensional analysis	p. 236
The perturbative method	p. 242
Diagrammatic series	p. 242
Loop expansion	p. 246
Evaluation of integrals and dimensional continuation	p. 250
Group theoretical factors	p. 259
Power counting	p. 261
Perturbative renormalization	p. 264
The renormalization group	p. 270
Renormalization flow	p. 270
Critical exponents	p. 280
From the Gaussian ultraviolet fixed point to the infrared critical point in dimension less than four	p. 282
Correlation functions at the critical point	p. 284
Expansion near the critical point	p. 290
Scaling laws below the critical temperature	p. 296
Corrections to scaling laws	p. 301
Deviation from the critical point in dimension lower than four	p. 301
Logarithmic corrections in dimension four	p. 303
Irrelevant operators	p. 307
Numerical results	p. 310
[varepsilon]-expansion of critical exponents	p. 311
Equation of state	p. 313
Amplitude ratios	p. 314
Three-dimensional results	p. 317
Multicritical points	p. 317
Notes	p. 326
Lattice gauge fields	p. 328
Generalities	p. 328
Presentation	p. 328
The continuous limit	p. 332
Order parameter and Elitzur's theorem	p. 341
Duality	p. 345
Structure of the phase diagram	p. 352
Mean field approximation	p. 352
Corrections to mean field and restoration of gauge invariance	p. 359
Discrete groups: 1/d expansion	p. 362
Continuous groups: computation of corrections	p. 365
Strong coupling expansions	p. 371
Convergence	p. 371
Character expansions	p. 374
Free energy	p. 380
String tension and roughening transition	p. 385
Mass spectrum	p. 390
Lattice fermions	p. 393
The doubling problem	p. 393
The Nielsen-Ninomiya theorem	p. 396
Staggered fermions	p. 399
Notes	p. 401
Index
Table of Contents provided by Syndetics. All Rights Reserved.

Statistical Field Theory

From Brownian Motion to Renormalization and Lattice Gauge Theory

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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