Equilibrium Statistical Physics

by Soni, Shivani

• ISBN13: 9789812560483
• ISBN10: 9812560483
• Edition: 3rd
• Format: Hardcover
• Copyright: 2014-08-01
• Publisher: World Scientific Pub Co Inc

Summary

- Each chapter contains a substantial number of exercises- A manual with a complete set of solutions to these problems is available under separate cover

Table of Contents

Preface to the First Edition	xi
Preface to the Second Edition	xiv
Preface Aire to the Third Edition	xv
1 Review of Thermodynamics	1	(28)
1.1 State Variables and Equations of State	1	(2)
1.2 Laws of Thermodynamics	3	(6)
1.2.1 First law	3	(2)
1.2.2 Second law	5	(4)
1.3 Thermodynamic Potentials	9	(3)
1.4 Gibbs-Duhem and Maxwell Relations	12	(2)
1.5 Response Functions	14	(2)
1.6 Conditions for Equilibrium and Stability	16	(2)
1.7 Magnetic Work	18	(2)
1.8 Thermodynamics of Phase Transitions	20	(4)
1.9 Problems	24	(5)
2. Statistical Ensembles	29	(34)
2.1 Isolated Systems: Microcanonical Ensemble	30	(5)
2.2 Systems at Fixed Temperature: Canonical Ensemble	35	(5)
2.3 Grand Canonical Ensemble	40	(3)
2.4 Quantum Statistics	43	(5)
2.4.1 Harmonic oscillator	44	(1)
2.4.2 Noninteracting fermions	44	(1)
2.4.3 Noninteracting bosons	45	(1)
2.4.4 Density matrix	46	(2)
2.5 Maximum Entropy Principle	48	(5)
2.6 Thermodynamic Variational Principles	53	(1)
2.6.1 Schottky defects in a crystal	53	(1)
2.7 Problems	54	(9)
3 Mean Field and Landau Theory	63	(46)
3.1 Mean Field Theory of the Ising Model	64	(3)
3.2 Bragg—Williams Approximation	67	(2)
3.3 A Word of Warning	69	(2)
3.4 Bethe Approximation	71	(3)
3.5 Critical Behavior of Mean Field Theories	74	(3)
3.6 Ising Chain: Exact Solution	77	(6)
3.7 Landau Theory of Phase Transitions	83	(3)
3.8 Symmetry Considerations	86	(4)
3.8.1 Potts model	87	(3)
3.9 Landau Theory of Tricritical Points	90	(4)
3.10 Landau—Ginzburg Theory for Fluctuations	94	(4)
3.11 Multicomponent Order Parameters: n-Vector Model	98	(2)
3.12 Problems	100	(9)
4 Applications of Mean Field Theory	109	(34)
4.1 Order—Disorder Transition	110	(4)
4.2 Maier--Saupe Model	114	(6)
4.3 Blume—Emery—Griffiths Model	120	(3)
4.4 Mean Field Theory of Fluids: van der Waals Approach	123	(6)
4.5 Spruce Budworm Model	129	(3)
4.6 A Non-Equilibrium System: Two Species Asymmetric Exclusion	132	(5)
4.7 Problems	137	(6)
5 Dense Gases and Liquids	143	(40)
5.1 Virial Expansion	145	(6)
5.2 Distribution Functions	151	(10)
5.2.1 Pair correlation function	151	(6)
5.2.2 BBGKY hierarchy	157	(1)
5.2.3 Ornstein—Zernike equation	158	(3)
5.3 Perturbation Theory	161	(2)
5.4 Inhomogeneous Liquids	163	(8)
5.4.1 Liquid—vapor interface	164	(5)
5.4.2 Capillary waves	169	(2)
5.5 Density-Functional Theory	171	(10)
5.5.1 Functional differentiation	171	(3)
5.5.2 Free-energy functionals and correlation functions	174	(5)
5.5.3 Applications	179	(2)
5.6 Problems	181	(2)
6 Critical Phenomena I	183	(54)
6.1 Model in Two Dimensions	184	(15)
6.1.1 Transfer matrix	184	(4)
6.1.2 Transformation to an interacting fermion problem	188	(3)
6.1.3 Calculation of eigenvalues	191	(3)
6.1.4 Thermodynamic functions	194	(5)
6.1.5 Concluding remarks	199	(1)
6.2 Series Expansions	199	(12)
6.2.1 High-temperature expansions	200	(6)
6.2.2 Low-temperature expansions	206	(1)
6.2.3 Analysis of series	206	(5)
6.3 Scaling	211	(7)
6.3.1 Thermodynamic considerations	211	(1)
6.3.2 Scaling hypothesis	212	(3)
6.3.3 Kadanoff block spins	215	(3)
6.4 Finite-Size Scaling	218	(5)
6.5 Universality	223	(3)
6.6 Kosterlitz—Thouless Transition	226	(7)
6.7 Problems	233	(4)
7 Critical Phenomena II: The Renormalization Group	237	(66)
7.1 The Ising Chain Revisited	238	(4)
7.2 Fixed Points	242	(6)
7.3 An Exactly Solvable Model: Ising Spins on a Diamond Fractal	248	(10)
7.4 Position Space Renormalization: Cumulant Method	258	(9)
7.4.1 First-order approximation	262	(2)
7.4.2 Second-order approximation	264	(3)
7.5 Other Position Space Renormalization (Troup Methods	267	(8)
7.5.1 Finite lattice methods	267	(1)
7.5.2 Adsorbed monolayers: Ising antiferromagnet	268	(4)
7.5.3 Monte Carlo renormalization	272	(3)
7.6 Phenomenological Renormalization Group	275	(4)
7.7 The &Expansion	279	(13)
7.7.1 The Gaussian model	281	(3)
7.7.2 The S4 model	284	(6)
7.7.3 Conclusion	290	(2)
Appendix: Second Order Cumulant Expansion	292	(3)
7.8 Problems	295	(8)
8 Stochastic Processes	303	(46)
8.1 Markov Processes and the Master Equation	304	(2)
8.2 Birth and Death Processes	306	(3)
8.3 Branching Processes	309	(4)
8.4 Fokker—Planck Equation	313	(3)
8.5 Fokker—Planck Equation with Several Variables: SIR Model	316	(5)
8.6 Jump Moments for Continuous Variables	321	(7)
8.6.1 Brownian motion	323	(3)
8.6.2 Rayleigh and Kramers equations	326	(2)
8.7 Diffusion, First Passage and Escape	328	(12)
8.7.1 Natural boundaries: The Kimura—Weiss model for genetic drift	329	(2)
8.7.2 Artificial boundaries	331	(1)
8.7.3 First passage time and escape probability	332	(5)
8.7.4 Kramers escape rate	337	(3)
8.8 Transformations of the Fokker—Planck Equation	340	(5)
8.8.1 Heterogeneous diffusion	340	(3)
8.8.2 Transformation to the Schrödinger equation	343	(2)
8.9 Problems	345	(4)
9 Simulations	349	(34)
9.1 Molecular Dynamics	350	(7)
9.1.1 Conservative molecular dynamics	351	(2)
9.1.2 Brownian dynamics	353	(2)
9.1.3 Data analysis	355	(2)
9.2 Monte Carlo Method	357	(8)
9.2.1 Discrete time Markov processes	358	(1)
9.2.2 Detailed balance and the Metropolis algorithm	359	(4)
9.2.3 Histogram methods	363	(2)
9.3 Data Analysis	365	(6)
9.3.1 Fluctuations	365	(2)
9.3.2 Error estimates	367	(1)
9.3.3 Extrapolation to the thermodynamic limit	368	(3)
9.4 The Hopfield Model of Neural Nets	371	(5)
9.5 Simulated Quenching and Annealing	376	(3)
9.6 Problems	379	(4)
10 Polymers and Membranes	383	(38)
10.1 Linear Polymers	384	(7)
10.1.1 The freely jointed chain	386	(3)
10.1.2 The Gaussian chain	389	(2)
10.2 Excluded Volume Effects: Flory Theory	391	(4)
10.3 Polymers and the n-Vector Model	395	(5)
10.4 Dense Polymer Solutions	400	(5)
10.5 Membranes	405	(13)
10.5.1 Phantom membranes	406	(3)
10.5.2 Self-avoiding membranes	409	(6)
10.5.3 Liquid membranes	415	(3)
10.6 Problems	418	(3)
11 Quantum Fluids	421	(40)
11.1 Bose Condensation	422	(8)
11.2 Superfluidity	430	(12)
11.2.1 Qualitative features of superfluidity	430	(9)
11.2.2 Bogoliubov theory of the 4He excitation spectrum	439	(3)
11.3 Superconductivity	442	(14)
11.3.1 Cooper problem	443	(2)
11.3.2 BCS ground state	445	(4)
11.3.3 Finite-temperature BCS theory	449	(4)
11.3.4 Landau–Ginzburg theory of superconductivity	453	(3)
11.4 Problems	456	(5)
12 Linear Response Theory	461	(52)
12.1 Exact Results	462	(10)
12.1.1 Generalized susceptibility and the structure factor	462	(7)
12.1.2 Thermodynamic properties	469	(1)
12.1.3 Sum rules and inequalities	470	(2)
12.2 Mean Field Response	472	(18)
12.2.1 Dielectric function of the electron gas	473	(2)
12.2.2 Weakly interacting Bose gas	475	(2)
12.2.3 Excitations of the Heisenberg ferromagnet	477	(3)
12.2.4 Screening and plasmons	480	(6)
12.2.5 Exchange and correlation energy	486	(1)
12.2.6 Phonons in metals	487	(3)
12.3 Entropy Production, the Kubo Formula, and the Onsager Relations for Transport Coefficients	490	(8)
12.3.1 Kubo formula	490	(2)
12.3.2 Entropy production and generalized currents and forces	492	(2)
12.3.3 Microscopic reversibility: Onsager relations	494	(4)
12.4 The Boltzmann Equation	498	(9)
12.4.1 Fields, drift and collisions	498	(2)
12.4.2 DC conductivity of a metal	500	(3)
12.4.3 Thermal conductivity and thermoelectric effects	503	(4)
12.5 Problems	507	(6)
13 Disordered Systems	513	(56)
13.1 Single-Particle States in Disordered Systems	515	(15)
13.1.1 Electron states in one dimension	516	(1)
13.1.2 Transfer matrix	517	(6)
13.1.3 Localization in three dimensions	523	(2)
13.1.4 Density of states	525	(5)
13.2 Percolation	530	(12)
13.2.1 Scaling theory of percolation	533	(3)
13.2.2 Series expansions and renormalization group	536	(4)
13.2.3 Rigidity percolation	540	(2)
13.2.4 Conclusion	542	(1)
13.3 Phase Transitions in Disordered Materials	542	(9)
13.3.1 Statistical formalism and the replica trick	544	(2)
13.3.2 Nature of phase transitions	546	(5)
13.4 Strongly Disordered Systems	551	(14)
13.4.1 Molecular glasses	552	(2)
13.4.2 Spin glasses	554	(4)
13.4.3 Sherrington—Kirkpatrick model	558	(7)
13.5 Problems	565	(4)
A Occupation Number Representation	569	(14)
Bibliography	583	(20)
Index	603