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| 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: General Adult
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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