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500 Pages
500 Pages
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27.64 x 20.32 x 2.57
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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.
Industry Reviews
"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
| Introduction | p. xi |
| Fundamentals of Statistical Physics | p. 1 |
| The Lectures--A Survey | p. 3 |
| The Journey: Many Different Approaches | p. 3 |
| The Main Sights | p. 5 |
| Is the Trip Worthwhile? | p. 9 |
| One Particle and Many | p. 11 |
| Formulation | p. 11 |
| The Ising Model | p. 12 |
| N Independent Particles--Quantum Description | p. 13 |
| Averages From Derivatives | p. 15 |
| N Independent Particles in a Box | p. 17 |
| Fluctuations Big and Small | p. 20 |
| The Problems of Statistical Physics | p. 21 |
| Gaussian Distributions | p. 29 |
| Introduction | p. 29 |
| One Variable | p. 29 |
| Many Gaussian Variables | p. 31 |
| Lattice Green Function | p. 33 |
| Gaussian Random Functions | p. 35 |
| Central Limit Theorem | p. 35 |
| Distribution of Energies | p. 36 |
| Large Deviations | p. 38 |
| On Almost Gaussian Integrals | p. 41 |
| Three Versions of Gaussian Problems | p. 42 |
| Quantum Mechanics and Lattices | p. 45 |
| All of Quantum Mechanics in One Brief Section | p. 45 |
| From d = 1 Models to Quantum Mechanics | p. 46 |
| An Example: The Linear Ising Chain | p. 48 |
| One-Dimensional Gaussian Model | p. 51 |
| Coherence Length | p. 56 |
| Operator Averages | p. 57 |
| Correlation Functions | p. 59 |
| Ising Correlations | p. 60 |
| Two-Dimensional Ising Model | p. 64 |
| Random Dynamics | p. 69 |
| Diffusion and Hopping | p. 71 |
| Random Walk on a Lattice | p. 71 |
| Formulating This Problem | p. 73 |
| The Diffusion of Probability and Particles | p. 76 |
| From Conservation to Hydrodynamic Equations | p. 79 |
| Distribution Functions | p. 83 |
| Cascade Processes and Securities Prices | p. 84 |
| Reprints on Dynamics | p. 91 |
| Forest and Witten: Smoke Particle Aggregates | p. 92 |
| Witten and Sander: Diffusion Limited Aggregation | p. 101 |
| Kadanoff: Chaos and Complexity | p. 105 |
| From Hops to Statistical Mechanics | p. 119 |
| Random Walk in Momentum | p. 120 |
| The Diffusion Equation Again | p. 123 |
| Time Dependence of Probability | p. 124 |
| Time Dependence in Deterministic Case | p. 126 |
| Equilibrium Solutions | p. 128 |
| Back to Collisions | p. 131 |
| From Fokker-Planck to Equilibrium | p. 133 |
| Properties of Fokker-Planck Equation | p. 135 |
| Reprints on Organization | p. 138 |
| Chao Tang et al.: Phase Organization | p. 139 |
| Bak et al.: Self-Organized Criticality | p. 143 |
| Carlson et al.: Singular Diffusion | p. 147 |
| Jaeger et al.: Experimental Studies | p. 151 |
| Correlations and Response | p. 155 |
| Time Independent Response | p. 155 |
| Hamiltonian Time-Dependence | p. 158 |
| Sum Rules | p. 161 |
| Non-Interacting Particles | p. 163 |
| Plasma Behavior | p. 164 |
| More Statistical Mechanics | p. 169 |
| Statistical Thermodynamics | p. 171 |
| The Chemical Potential Defined | p. 171 |
| Barometer Formula | p. 173 |
| Sharing Energy | p. 174 |
| Ensemble Theory | p. 179 |
| Temperatures and Energy Flow | p. 182 |
| Fermi, Bose, and Other | p. 187 |
| Quantum Formulation | p. 187 |
| Statistical Mechanics of Non-Interacting Degenerate Particles | p. 188 |
| The Non-Degenerate Limit | p. 191 |
| Degenerate Fermions | p. 192 |
| Degenerate Bosons I. Photons and Phonons | p. 196 |
| Degenerate Bosons II. One-Dimensional Phonons | p. 198 |
| Degenerate Bosons III. Bose Phase Transition | p. 201 |
| Entropies | p. 203 |
| Phase Transitions | p. 207 |
| Overview of Phase Transitions | p. 209 |
| Thermodynamic Phases | p. 209 |
| Phase Transitions | p. 210 |
| Two Kinds of Transitions | p. 211 |
| Back to the Ising Model | p. 214 |
| Mean Field Theory of Magnets | p. 215 |
| The Phases | p. 216 |
| Low Temperature Result | p. 218 |
| Free Energy Selection Argument | p. 219 |
| Behaviors of Different Phases | p. 221 |
| Mean Field Theory of Critical Behavior | p. 225 |
| The Infinite Range Model | p. 226 |
| Mean Field Theory Near the Critical Point | p. 227 |
| Critical Indices | p. 230 |
| Scaling Function for Magnetization | p. 231 |
| Spatial Correlations | p. 232 |
| Analyticity | p. 238 |
| Mean Field Theory for the Free Energy | p. 239 |
| When Mean Field Theory Fails | p. 242 |
| Continuous Phase Transitions | p. 247 |
| Historical Background | p. 247 |
| Widom Scaling Theory | p. 248 |
| The Ising Model: Rescaled | p. 252 |
| Fixed Points | p. 257 |
| Phenomenology of Scaling Fields | p. 258 |
| Theory of Scaling Fields | p. 259 |
| Scaling Relations for Operators | p. 262 |
| Transforming Operators | p. 266 |
| Universality | p. 266 |
| Operator Product Expansions | p. 267 |
| Reprints on Critical Correlations | p. 268 |
| Kadanoff: Correlations Along a Line | p. 269 |
| Kadanoff-Wegner: Marginal Behavior | p. 274 |
| Renormalization in One Dimension | p. 279 |
| Introduction | p. 279 |
| Decimation | p. 279 |
| The Ising Example | p. 280 |
| Phase Diagrams, Flow Diagrams, and the Coherence Length | p. 281 |
| The Gaussian Model | p. 283 |
| Analysis of Recursion Relation | p. 284 |
| Fixed Point Analysis for the Gaussian Model | p. 285 |
| Two-Dimensional Ising Model | p. 288 |
| Real Space Renormalization Techniques | p. 291 |
| Introduction | p. 291 |
| Decimation: An Exact Calculation | p. 292 |
| The Method of Neglect | p. 294 |
| Potential Moving | p. 295 |
| Further Work | p. 298 |
| Reprints on Real Space RG | p. 298 |
| Niemeijer and van Leeuwen: Triangular Lattice R.G. | p. 299 |
| David Nelson's Early Summary | p. 303 |
| Kadanoff: Bond-moving, and a Variational Method | p. 308 |
| Kadanoff: Migdal's Simple and Versatile Method | p. 312 |
| Migdal's Original Papers | p. 348 |
| Duality | p. 359 |
| Doing Sums | p. 359 |
| Two Dimensions | p. 361 |
| Direct Coupling and Dual Coupling | p. 363 |
| Two-Dimensional Calculation | p. 365 |
| Ising Model | p. 368 |
| XY is Connected to SOS | p. 369 |
| Gaussian goes into Gaussian | p. 371 |
| Dual Correlations | p. 371 |
| Planar Model and Coulomb Systems | p. 377 |
| Why Study a Planar Model? | p. 377 |
| One-Dimensional Case | p. 379 |
| Phases of the Planar Model | p. 380 |
| The Gaussian Approximation | p. 382 |
| Two-Dimensional Coulomb Systems | p. 386 |
| Multipole Expansion | p. 387 |
| Reprint on Spin Waves | p. 390 |
| V. L. Berezinskii: An Overview of Problems with Continuous Symmetry | p. 391 |
| XY Model, Renormalization, and Duality | p. 399 |
| Plan of Action | p. 399 |
| Villain Representation of the Basic Bonds | p. 400 |
| Duality Transformation | p. 401 |
| Two Limits | p. 402 |
| Vortex Representation | p. 403 |
| The Magnetically Charged System | p. 405 |
| Correlation Calculation | p. 408 |
| The Renormalization Calculation | p. 409 |
| Spatial Averages | p. 411 |
| The Actual Renormalization | p. 413 |
| Reprints on Planar Model | p. 415 |
| The Kosterlitz-Thouless Theory | p. 416 |
| Kosterlitz: On Renormalization of the Planar Model | p. 439 |
| Jorge V. Jose, Leo P. Kadanoff, Scott Kirkpatrick, David R. Nelson: Renormalization and Vortices | p. 454 |
| Index | p. 479 |
| Table of Contents provided by Syndetics. All Rights Reserved. |
ISBN: 9789810237646
ISBN-10: 9810237642
Published: 3rd May 2000
Format: Paperback
Language: English
Number of Pages: 500
Audience: College, Tertiary and University
Publisher: World Scientific Publishing Co Pte Ltd
Country of Publication: GB
Dimensions (cm): 27.64 x 20.32 x 2.57
Weight (kg): 1.02
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