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Statistical Physics : Statics, Dynamics and Renormalization - Leo P. Kadanoff

Statistical Physics

Statics, Dynamics and Renormalization

Paperback Published: 8th May 2000
ISBN: 9789810237646
Number Of Pages: 483

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The material presented in this invaluable textbook has been tested in two courses. One of these is a graduate-level survey of statistical physics; the other, a rather personal perspective on critical behavior. Thus, this book defines a progression starting at the book-learning part of graduate education and ending in the midst of topics at the research level. To supplement the research-level side the book includes some research papers. Several of these are classics in the field, including a suite of six works on self-organized criticality and complexity, a pair on diffusion-limited aggregation, some papers on correlations near critical points, a few of the basic sources on the development of the real-space renormalization group, and several papers on magnetic behavior in a plain geometry. In addition, the author has included a few of his own papers.

"Leo Kadanoff has been a pioneer in the elucidations of cooperative phenomena, in both equilibrium and nonequilibrium systems. His insights are deep and he expresses them lucidly. This book is full of such goodies and is a pleasure to read and contemplate. Very highly recommended for both experts and novices." Joel L Lebowitz Rutgers University "Leo Kadanoff is one of the deep thinkers in statistical physics and that is apparent on almost every page of his "Statistical Physics: Statics, Dynamics, and Renormalization". This is a mixture of pedagogy, history (including reprints of classical or especially apt papers), and original thoughts, full of wisdom and with many startling insights. It is based in part on lectures Professor Kadanoff has given in graduate courses at the University of Chicago. His students and other attendees were most fortunate; I wish I had been among them!" Benjamin Widom Cornell University "This long-awaited book is an elegant and rather personal account of statistical mechanics that stands out form the pack for many reasons. Not only does it conspicuously emphasize the different treatments afforded to different levels of description, but it also discusses the connection between dynamical systems theory and the foundations of statistical mechanics. Kadanoff's pioneering contributions to phase transitions and the renormalization group are covered in a marvellous retrospective that will be engaging to novice and expert alike. And the book is rounded out with an interesting selection of advanced topics and reprints, that will make it an essential part of a modern graduate course on statistical physics." Nigel Goldenfeld University of Illinois, Urbana-Champaign "From a scientist reknown for his work, his lectures and very articulate opinions, this book is a completely new attempt to reconsider the traditional teaching of the whole subject of statistical physics. Avoiding any heavy formalism, Prof Kadanoff has chosen to introduce the main concepts through simple models which are far superior for understanding the subject in real depth. A little more than half of the book is devoted to the theory of phase transitions, a subject which owes so much to the author. Scaling theory and renormalization group are described in a remarkably simple and lucid manner. This book will be greatly enjoyed by its readers, academics and students all together." Edouard Brezin Ecole Normale de Superieure, Paris "Leo Kadanoff's, Statistical Physics: Statistics, Dynamics and Renormalization, offers an exciting new textbook choice for those teaching a course in statistical physics. In many ways the book breaks new ground in presentation, style, and choice of topics. It will be particularly appreciated for its emphasis on providing tools appropriate to the most active and important new research areas in statistical physics ... Kadanoff's lucid exposition and organization are clearly informed by his own unique view of the subject gained from a life-time of creative thought and profound contributions in statistical physics." Ed Ott University of Maryland "... this masterly written book on modern statistical physics by the old master in the field can be highly recommended as an excellent graduate textbook on statistical physics as well as a source on research in this very progressive field of nonlinear science." Mathematics Abstracts "... Statistical Physics is a collection of valuable essays and papers. Both the text and the reprints display Kadanoff's ingenuity, imagination, and clarity. They're worth having and reading." Physics Today, 2001

Introductionp. xi
Fundamentals of Statistical Physicsp. 1
The Lectures--A Surveyp. 3
The Journey: Many Different Approachesp. 3
The Main Sightsp. 5
Is the Trip Worthwhile?p. 9
One Particle and Manyp. 11
Formulationp. 11
The Ising Modelp. 12
N Independent Particles--Quantum Descriptionp. 13
Averages From Derivativesp. 15
N Independent Particles in a Boxp. 17
Fluctuations Big and Smallp. 20
The Problems of Statistical Physicsp. 21
Gaussian Distributionsp. 29
Introductionp. 29
One Variablep. 29
Many Gaussian Variablesp. 31
Lattice Green Functionp. 33
Gaussian Random Functionsp. 35
Central Limit Theoremp. 35
Distribution of Energiesp. 36
Large Deviationsp. 38
On Almost Gaussian Integralsp. 41
Three Versions of Gaussian Problemsp. 42
Quantum Mechanics and Latticesp. 45
All of Quantum Mechanics in One Brief Sectionp. 45
From d = 1 Models to Quantum Mechanicsp. 46
An Example: The Linear Ising Chainp. 48
One-Dimensional Gaussian Modelp. 51
Coherence Lengthp. 56
Operator Averagesp. 57
Correlation Functionsp. 59
Ising Correlationsp. 60
Two-Dimensional Ising Modelp. 64
Random Dynamicsp. 69
Diffusion and Hoppingp. 71
Random Walk on a Latticep. 71
Formulating This Problemp. 73
The Diffusion of Probability and Particlesp. 76
From Conservation to Hydrodynamic Equationsp. 79
Distribution Functionsp. 83
Cascade Processes and Securities Pricesp. 84
Reprints on Dynamicsp. 91
Forest and Witten: Smoke Particle Aggregatesp. 92
Witten and Sander: Diffusion Limited Aggregationp. 101
Kadanoff: Chaos and Complexityp. 105
From Hops to Statistical Mechanicsp. 119
Random Walk in Momentump. 120
The Diffusion Equation Againp. 123
Time Dependence of Probabilityp. 124
Time Dependence in Deterministic Casep. 126
Equilibrium Solutionsp. 128
Back to Collisionsp. 131
From Fokker-Planck to Equilibriump. 133
Properties of Fokker-Planck Equationp. 135
Reprints on Organizationp. 138
Chao Tang et al.: Phase Organizationp. 139
Bak et al.: Self-Organized Criticalityp. 143
Carlson et al.: Singular Diffusionp. 147
Jaeger et al.: Experimental Studiesp. 151
Correlations and Responsep. 155
Time Independent Responsep. 155
Hamiltonian Time-Dependencep. 158
Sum Rulesp. 161
Non-Interacting Particlesp. 163
Plasma Behaviorp. 164
More Statistical Mechanicsp. 169
Statistical Thermodynamicsp. 171
The Chemical Potential Definedp. 171
Barometer Formulap. 173
Sharing Energyp. 174
Ensemble Theoryp. 179
Temperatures and Energy Flowp. 182
Fermi, Bose, and Otherp. 187
Quantum Formulationp. 187
Statistical Mechanics of Non-Interacting Degenerate Particlesp. 188
The Non-Degenerate Limitp. 191
Degenerate Fermionsp. 192
Degenerate Bosons I. Photons and Phononsp. 196
Degenerate Bosons II. One-Dimensional Phononsp. 198
Degenerate Bosons III. Bose Phase Transitionp. 201
Entropiesp. 203
Phase Transitionsp. 207
Overview of Phase Transitionsp. 209
Thermodynamic Phasesp. 209
Phase Transitionsp. 210
Two Kinds of Transitionsp. 211
Back to the Ising Modelp. 214
Mean Field Theory of Magnetsp. 215
The Phasesp. 216
Low Temperature Resultp. 218
Free Energy Selection Argumentp. 219
Behaviors of Different Phasesp. 221
Mean Field Theory of Critical Behaviorp. 225
The Infinite Range Modelp. 226
Mean Field Theory Near the Critical Pointp. 227
Critical Indicesp. 230
Scaling Function for Magnetizationp. 231
Spatial Correlationsp. 232
Analyticityp. 238
Mean Field Theory for the Free Energyp. 239
When Mean Field Theory Failsp. 242
Continuous Phase Transitionsp. 247
Historical Backgroundp. 247
Widom Scaling Theoryp. 248
The Ising Model: Rescaledp. 252
Fixed Pointsp. 257
Phenomenology of Scaling Fieldsp. 258
Theory of Scaling Fieldsp. 259
Scaling Relations for Operatorsp. 262
Transforming Operatorsp. 266
Universalityp. 266
Operator Product Expansionsp. 267
Reprints on Critical Correlationsp. 268
Kadanoff: Correlations Along a Linep. 269
Kadanoff-Wegner: Marginal Behaviorp. 274
Renormalization in One Dimensionp. 279
Introductionp. 279
Decimationp. 279
The Ising Examplep. 280
Phase Diagrams, Flow Diagrams, and the Coherence Lengthp. 281
The Gaussian Modelp. 283
Analysis of Recursion Relationp. 284
Fixed Point Analysis for the Gaussian Modelp. 285
Two-Dimensional Ising Modelp. 288
Real Space Renormalization Techniquesp. 291
Introductionp. 291
Decimation: An Exact Calculationp. 292
The Method of Neglectp. 294
Potential Movingp. 295
Further Workp. 298
Reprints on Real Space RGp. 298
Niemeijer and van Leeuwen: Triangular Lattice R.G.p. 299
David Nelson's Early Summaryp. 303
Kadanoff: Bond-moving, and a Variational Methodp. 308
Kadanoff: Migdal's Simple and Versatile Methodp. 312
Migdal's Original Papersp. 348
Dualityp. 359
Doing Sumsp. 359
Two Dimensionsp. 361
Direct Coupling and Dual Couplingp. 363
Two-Dimensional Calculationp. 365
Ising Modelp. 368
XY is Connected to SOSp. 369
Gaussian goes into Gaussianp. 371
Dual Correlationsp. 371
Planar Model and Coulomb Systemsp. 377
Why Study a Planar Model?p. 377
One-Dimensional Casep. 379
Phases of the Planar Modelp. 380
The Gaussian Approximationp. 382
Two-Dimensional Coulomb Systemsp. 386
Multipole Expansionp. 387
Reprint on Spin Wavesp. 390
V. L. Berezinskii: An Overview of Problems with Continuous Symmetryp. 391
XY Model, Renormalization, and Dualityp. 399
Plan of Actionp. 399
Villain Representation of the Basic Bondsp. 400
Duality Transformationp. 401
Two Limitsp. 402
Vortex Representationp. 403
The Magnetically Charged Systemp. 405
Correlation Calculationp. 408
The Renormalization Calculationp. 409
Spatial Averagesp. 411
The Actual Renormalizationp. 413
Reprints on Planar Modelp. 415
The Kosterlitz-Thouless Theoryp. 416
Kosterlitz: On Renormalization of the Planar Modelp. 439
Jorge V. Jose, Leo P. Kadanoff, Scott Kirkpatrick, David R. Nelson: Renormalization and Vorticesp. 454
Indexp. 479
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9789810237646
ISBN-10: 9810237642
Audience: General
Format: Paperback
Language: English
Number Of Pages: 483
Published: 8th May 2000
Publisher: World Scientific Publishing Co Pte Ltd
Country of Publication: SG
Dimensions (cm): 26.21 x 19.3  x 2.62
Weight (kg): 1.02

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