Statistical Mechanics From Thermodynamics to the Renormalization Group

Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Preface
SECTION I: Structure of Statistical Mechanics
	CHAPTER 1: Thermodynamics: Equilibrium, energy, entropy
		1.1. SYSTEMS, BOUNDARIES, AND VARIABLES
		1.2. INTERNAL ENERGY: WORK AND HEAT
		1.3. CLAUSIUS ENTROPY: IRREVERSIBILITY, DISORGANIZATION
		1.4. THERMODYNAMIC POTENTIALS
		1.5. FREE ENERGY AND DISSIPATED ENERGY
		1.6. CHEMICAL POTENTIAL AND OPEN SYSTEMS
		1.7. MAXWELL RELATIONS
		1.8. RESPONSE FUNCTIONS
		1.9. HEAT CAPACITY OF MAGNETIC SYSTEMS
		1.10. EXTENSIVITY OF ENTROPY, SACKUR-TETRODE FORMULA
		1.11. BOLTZMANN ENTROPY: CONNECTION WITH MICROSCOPICS
		1.12. FLUCTUATIONS AND STABILITY
		1.13. LIMITATIONS OF THERMODYNAMICS
	CHAPTER 2: From mechanics to statistical mechanics
		2.1. MICROSTATES—THE MANY
		2.2. STATE VARIABLES—THE FEW
		2.3. ENTROPY, THE BRIDGE BETWEEN MICRO AND MACRO
		2.4. FLUCTUATIONS: GATEWAY TO ENSEMBLES AND PROBABILITY
		2.5. ENSEMBLE FLOWS IN PHASE SPACE, LIOUVILLE’S THEOREM
		2.6. BIRKHOFF’S THEOREM
		2.7. THE ROLE OF PROBABILITY
	CHAPTER 3: Probability theory
		3.1. EVENTS, SAMPLE SPACE, AND PROBABILITY
		3.2. COMBINING PROBABILITIES, CONDITIONAL PROBABILITY
		3.3. COMBINATORICS
		3.4. EXAMPLES INVOLVING DISCRETE PROBABILITIES
		3.5. RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS
		3.6. CENTRAL LIMIT THEOREM, LAW OF LARGE NUMBERS
		3.7. CUMULANTS AND CHARACTERISTIC FUNCTIONS
	CHAPTER 4: Ensemble theory
		4.1. CLASSICAL ENSEMBLES: PROBABILITY DENSITY FUNCTIONS
		4.2. THE THERMODYNAMIC LIMIT: EXISTENCE OF EXTENSIVITY
		4.3. CONVEXITY AND STABILITY
		4.4. QUANTUM ENSEMBLES: PROBABILITY DENSITY OPERATORS
SECTION II: Applications of Equilibrium Statistical Mechanics
	CHAPTER 5: Ideal systems
		5.1. THE MAXWELL SPEED DISTRIBUTION
		5.2. PARAMAGNETS
		5.3. HARMONIC OSCILLATORS, QUANTUM AND CLASSICAL
		5.4. DIATOMIC GASES
		5.5. IDENTICAL FERMIONS AND BOSONS
		5.6. DEGENERATE FERMI GAS: T = 0 AND 0 < T<< TF
		5.7. DEGENERACY PRESSURE IN THE LIFE OF STARS
		5.8. CAVITY RADIATION
		5.9. DEGENERATE BOSE GAS, BOSE-EINSTEIN CONDENSATION
	CHAPTER 6: Interacting systems
		6.1. THE MAYER CLUSTER EXPANSION
		6.2. VIRIAL EXPANSION, VAN DER WAALS EQUATION OF STATE
		6.3. CUMULANT EXPANSION OF THE FREE ENERGY
		6.4. THE TONKS AND TAKAHASHI GASES
		6.5. THE ONE-DIMENSIONAL ISING MODEL
		6.6. SCATTERING, FLUCTUATIONS, AND CORRELATIONS
		6.7. ORNSTEIN-ZERNIKE THEORY OF CRITICAL CORRELATIONS
	CHAPTER 7: Phase transitions and critical phenomena
		7.1. PHASE COEXISTENCE, GIBBS PHASE RULE
		7.2. THE CLASSIFICATION OF PHASE TRANSITIONS
		7.3. VAN DER WAALS LIQUID-GAS PHASE TRANSITION
		7.4. A BESTIARY OF CRITICAL EXPONENTS: α, β, γ, δ
		7.5. WEISS MOLECULAR FIELD THEORY OF FERROMAGNETISM
		7.6. THE CRITICAL CORRELATION EXPONENTS: v, n
		7.7. LANDAU THEORY OF PHASE TRANSITIONS
		7.8. MEAN-FIELD THEORY: UNCORRELATED FLUCTUATIONS
		7.9. WHEN IS MEAN FIELD THEORY EXACT?
		7.10. THE TWO-DIMENSIONAL ISING MODEL
		7.11. CRITICAL EXPONENT INEQUALITIES
		7.12. THE IMPOSSIBILITY OF PHASES IN ONE DIMENSION
	CHAPTER 8: Scaling theories and the renormalization group
		8.1. THE WIDOM SCALING HYPOTHESIS
		8.2. KADANOFF SCALING THEORY: SCALING EXPONENTS
		8.3. RENORMALIZATION: A FIRST LOOK
		8.4. THE RENORMALIZATION GROUP
		8.5. REAL-SPACE RENORMALIZATION
		8.6. WILSON RENORMALIZATION GROUP IN A NUTSHELL
APPENDIX A: Physical constants
APPENDIX B: Useful integrals
APPENDIX C: Classical mechanics
APPENDIX D: Quantum mechanics of identical particles
APPENDIX E: Topics in magnetism
APPENDIX F: The method of the most probable distribution
Bibliography
Index