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This second edition extends and improves on the first, already an acclaimed and original treatment of statistical concepts insofar as they impact theoretical physics and form the basis of modern thermodynamics. This book illustrates through myriad examples the principles and logic used in extending the simple laws of idealized Newtonian physics and quantum physics into the real world of noise and thermal fluctuations.In response to the many helpful comments by users of the first edition, important features have been added in this second, new and revised edition. These additions allow a more coherent picture of thermal physics to emerge. Benefiting from the expertise of the new co-author, the present edition includes a detailed exposition - occupying two separate chapters - of the renormalization group and Monte-Carlo numerical techniques, and of their applications to the study of phase transitions. Additional figures have been included throughout, as have new problems. A new Appendix presents fully worked-out solutions to representative problems; these illustrate various methodologies that are peculiar to physics at finite temperatures, that is, to statistical physics.This new edition incorporates important aspects of many-body theory and of phase transitions. It should better serve the contemporary student, while offering to the instructor a wider selection of topics from which to craft lectures on topics ranging from thermodynamics and random matrices to thermodynamic Green functions and critical exponents, from the propagation of sound in solids and fluids to the nature of quasiparticles in quantum liquids and in transfer matrices.
| Preface to Second Edition | p. xi |
| Preface to First Edition | p. xiii |
| Introduction: Theories of Thermodynamics, Kinetic Theory and Statistical Mechanics | p. xvii |
| Elementary Concepts in Statistics and Probability | p. 1 |
| Random Variables and Their Distributions | p. 1 |
| The Binomial Distribution | p. 2 |
| Length of a Winning Streak | p. 4 |
| Brownian Motion and the Random Walk | p. 5 |
| Poisson versus Normal (Gaussian) Distributions | p. 6 |
| Central Limit Theorem (CLT) | p. 10 |
| Multinomial Distributions, Statistical Thermodynamics | p. 13 |
| The Barometer Equation | p. 15 |
| Other Distributions | p. 16 |
| The Ising Model and the Lattice Gas | p. 19 |
| Physical Applications of the Binary Model | p. 19 |
| Some Background and Motivation | p. 20 |
| First-Principles Statistical Theory of Paramagnetism | p. 21 |
| More on Entropy and Energy | p. 24 |
| Some Other Relevant Thermodynamic Functions | p. 25 |
| Mean-Field Theory, Stable and Metastable Solutions | p. 26 |
| The Lattice Gas | p. 30 |
| The Nearest-Neighbor Chain: Thermodynamics in 1D | p. 31 |
| The Disordered Ising Chain | p. 32 |
| Other Magnetic Systems in One Dimension | p. 32 |
| Elements of Thermodynamics | p. 36 |
| The Scope of Thermodynamics | p. 36 |
| Equations of State and Some Definitions | p. 37 |
| Maxwell Relations | p. 40 |
| Three Important Laws of Thermodynamics | p. 40 |
| The Second Derivatives of the Free Energy | p. 43 |
| Phase Diagrams for the van der Waals Gas | p. 44 |
| Clausius-Clapeyron Equation | p. 48 |
| Phase Transitions | p. 50 |
| The Carnot Cycle | p. 54 |
| Superconductivity | p. 57 |
| Statistical Mechanics | p. 60 |
| An Axiomatic Approach and the Ergodic Hypothesis | p. 60 |
| The Formalism - and a False Start | p. 62 |
| Gibbs' Paradox and Its Remedy | p. 65 |
| The Gibbs Factor | p. 68 |
| The Grand Ensemble | p. 69 |
| Non-Ideal Gas and the 2-Body Correlation Function | p. 71 |
| The Virial Equation of State | p. 73 |
| Weakly Non-Ideal Gas | p. 74 |
| Two-body Correlations | p. 77 |
| Configurational Partition Function in 1D | p. 82 |
| One Dimension versus Two | p. 84 |
| Two Dimensions versus Three: The Debye-Waller Factors | p. 86 |
| Specific Heat of Quasi-Ideal Dilute Atomic and Diatomic Gases | p. 90 |
| Nanophysics and Inhomogeneity | p. 93 |
| The World of Bosons | p. 94 |
| Quantum "Statistics" | p. 94 |
| Two Types of Bosons and Their Operators | p. 94 |
| Number Representation and the Many-Body Problem | p. 97 |
| The Adiabatic Process and Conservation of Entropy | p. 99 |
| Many-Body Perturbations | p. 100 |
| Photons | p. 101 |
| Phonons | p. 105 |
| Ferromagnons | p. 107 |
| Conserved Bosons and the Ideal Bose Gas | p. 110 |
| Nature of "Ideal" Bose-Einstein Condensation | p. 113 |
| Ideal Bose-Einstein Condensation in Low Dimensions | p. 115 |
| Consequences of a Hard Core Repulsion in 1D | p. 118 |
| Bosons in 3D Subject to Weak Two-Body Forces | p. 121 |
| Superfluid Helium (He II) | p. 126 |
| All About Fermions: Theories of Metals, Superconductors, Semiconductors | p. 131 |
| Fermi-Dirac Particles | p. 131 |
| Slater Determinant: The Ground State | p. 132 |
| Ideal Spinless Fermi-Dirac Gas | p. 133 |
| Ideal Fermi-Dirac Gas with Spin | p. 135 |
| Fermi Integrals | p. 136 |
| Thermodynamic Functions of an Ideal Metal | p. 137 |
| Quasiparticles and Elementary Excitations | p. 140 |
| Semiconductor Physics: Electrons and Holes | p. 142 |
| n-Type Semiconductor Physics: The Statistics | p. 143 |
| Correlations and the Coulomb Repulsion | p. 144 |
| Miscellaneous Properties of Semiconductors | p. 147 |
| Aspects of Superconductivity: Cooper Pairs | p. 149 |
| Aspects of BCS Theory | p. 152 |
| Contemporary Developments in Superconductivity | p. 158 |
| Kinetic Theory | p. 160 |
| Scope of This Chapter | p. 160 |
| Quasi-Equilibrium Flows and the Second Law | p. 161 |
| The Collision Integral | p. 162 |
| Approach to Equilibrium of a "Classical" Non-Ideal Gas | p. 165 |
| A New Look at "Quantum Statistics" | p. 168 |
| Master Equation: Application to Radioactive Decay | p. 169 |
| Boltzmann Equation | p. 171 |
| Electrical Currents in a Low-Density Electron Gas | p. 174 |
| Diffusion and the Einstein Relation | p. 176 |
| Electrical Conductivity of Metals | p. 177 |
| Exactly Solved "Backscattering" Model | p. 178 |
| Electron-Phonon Scattering | p. 180 |
| Approximating the Boltzmann Equation | p. 181 |
| Crossed Electric and Magnetic Fields | p. 183 |
| Propagation of Sound Waves in Fluids | p. 184 |
| The Calculations and Their Result | p. 189 |
| The Transfer Matrix | p. 195 |
| The Transfer Matrix and the Thermal Zipper | p. 195 |
| Opening and Closing a "Zipper Ladder" or Polymer | p. 198 |
| The Full Zipper (N > 2) | p. 203 |
| The Transfer Matrix and Gaussian Potentials | p. 204 |
| Transfer Matrix in the Ising Model | p. 205 |
| The Ising Ladder or Polymer | p. 207 |
| Ising Model on the Isotropic Square Lattice (2D) | p. 209 |
| The Phase Transition | p. 214 |
| A Question of Long-Range Order | p. 216 |
| Ising Model in 2D and 3D | p. 218 |
| Antiferromagnetism and Frustration | p. 219 |
| Maximal Frustration | p. 222 |
| Separable Model Spin-Glass without Frustration | p. 224 |
| Critical Phenomena and Critical Exponents | p. 225 |
| Potts Models | p. 229 |
| Monte Carlo and Other Computer Simulation Methods | p. 232 |
| Numerical Methods in Statistical Mechanics | p. 232 |
| Molecular Dynamics | p. 232 |
| Stochastic Processes | p. 234 |
| Transition Rates and the Master Equation | p. 235 |
| Monte Carlo Moves | p. 237 |
| Applications of ARM and DOMC | p. 241 |
| Monte Carlo Estimates of Thermal Averages | p. 241 |
| Equilibration Times | p. 243 |
| Discrete Variables | p. 245 |
| Continuous Thermodynamic Functions and Histogram Methods | p. 246 |
| Phase Transitions | p. 249 |
| MC Calculation of Critical Exponents: Finite-Size Scaling | p. 249 |
| Critical Phenomena and the Renormalization Group | p. 254 |
| The Problem with Mean-Field Theories | p. 254 |
| Block-Spin Transformations for the Ising Model | p. 256 |
| Effect of Renormalization on the Spin Configurations | p. 258 |
| Renormalization of the Correlation Length | p. 260 |
| Mathematical Form of the RG Transformation | p. 260 |
| Effective or "Renormalized" Interactions | p. 261 |
| A Simple Example: The One-Dimensional Ising Model | p. 263 |
| Renormalization Trajectories | p. 265 |
| RG Trajectories and Critical Properties | p. 267 |
| Mathematical Analysis of RG Trajectories Near a Fixed Point | p. 268 |
| Calculating the Other Critical Exponents from the Eigenvalue Exponents | p. 270 |
| Exponent Identities | p. 271 |
| Calculating Values for the Eigenvalue Exponents Using MC Simulations | p. 272 |
| First-Order Transitions and Discontinuity Fixed Points | p. 276 |
| Calculation of the Renormalized Couplings | p. 277 |
| Some Uses of Quantum Field Theory in Statistical Physics | p. 279 |
| Outline of the Chapter | p. 279 |
| Diffusion on a Lattice: Standard Formulation | p. 280 |
| Diffusion as Expressed in QFT | p. 282 |
| Diffusion plus One-Body Recombination Processes | p. 285 |
| Diffusion and Two-Body Recombination Processes | p. 286 |
| Questions Concerning Long-Range Order | p. 288 |
| Mermin-Wagner Theorem | p. 290 |
| Proof of Bogolubov Inequality | p. 293 |
| Correlation Functions and the Free Energy | p. 294 |
| Introduction to Thermodynamic Green's Functions | p. 297 |
| Solutions to Selected Problems | p. 305 |
| Bibliography | p. 327 |
| Index | p. 331 |
| Table of Contents provided by Ingram. All Rights Reserved. |
ISBN: 9789812779090
ISBN-10: 9812779094
Published: 5th March 2008
Format: Paperback
Language: English
Number of Pages: 358
Audience: College, Tertiary and University
Publisher: World Scientific Publishing Co Pte Ltd
Country of Publication: GB
Edition Number: 2
Edition Type: Revised
Dimensions (cm): 24.41 x 16.99 x 1.88
Weight (kg): 0.62
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