Introduction to statistical physics

Cover ......Page 1
Graduate Texts in Contemporary Physics ......Page 2
Title: Introduction to Statistical Physics by Silvio R. A. Salinas ......Page 4
© 2001 Springer-Verlag ......Page 5
Preface ......Page 6
Contents ......Page 10
1. Introduction to Statistical Methods ......Page 14
1.1 The random walk in one dimension ......Page 15
1.2 Mean values and standard deviations ......Page 17
1.3 Gaussian limit of the binomial distribution ......Page 19
1.4 Distribution of several random variables: Continuous distributions ......Page 22
1.5 Probability distribution for the generalized random walk in one dimension. The Gaussian limit ......Page 25
Exercises ......Page 28
2. Statistical Description of a Physical System ......Page 32
2.1 Specification of the microscopic states of a quantum system ......Page 33
2.2 Specification of the microscopic state of a classical system of particles ......Page 38
2.3 Ergodic hyphotesis and fundamental postulate of statistical mechanics ......Page 42
2.4 Formulation of statistical mechanics for quantum systems ......Page 46
Exercises ......Page 48
3.1 Postulates of equilibrium thermodynamics ......Page 52
3.2 Intensive parameters of thermodynamics ......Page 54
3.3 Equilibrium between two thermodynamic systems ......Page 57
3.5 Thermodynamic derivatives of physical interest ......Page 60
3.6 Thermodynamic potentials ......Page 61
3.7 The Maxwell relations ......Page 65
3.8 Variational principles of thermodynamics ......Page 69
Exercises ......Page 72
4. Microcanonical Ensemble ......Page 74
4.1 Thermal interaction between two microscopic systems ......Page 75
4.2 Thermal and mechanical interaction between two systems ......Page 78
4.3 Connection between the microcanonical ensemble and thermodynamics ......Page 80
4.4 Classical monatomic ideal gas ......Page 92
Exercises ......Page 95
5. Canonical Ensemble ......Page 98
5.1 Ideal paramagnet of spin 1/2 ......Page 104
5.2 Solid of Einstein ......Page 106
5.3 Particles with two energy levels ......Page 108
5.4 The Boltzmann gas ......Page 110
Exercises ......Page 111
6. The Classical Gas in the Canonical Formalism ......Page 116
6.1 Ideal classical monatomic gas ......Page 118
6.2 The Maxwell-Boltzmann distribution ......Page 120
6.3 The theorem of equipartition of energy ......Page 121
6.4 The classical monatomic gas of particles ......Page 122
6.5 The thermodynamic limit of a continuum system ......Page 126
Exercises ......Page 130
7. The Grand Canonical and Pressure Ensembles ......Page 134
7.1 The pressure ensemble ......Page 135
7.2 The grand canonical ensemble ......Page 140
Exercises ......Page 150
8. The Ideal Quantum Gas ......Page 154
8.1 Orbitals of a free particle ......Page 156
8.2 Formulation of the statistical problem ......Page 159
8.3 Classi cal limit ......Page 162
8.4 Diluted gas of diatomic molecules ......Page 167
Exercises ......Page 170
9. The Ideal Fermi Gas ......Page 174
9.1 Completely degenerate ideal Fermi gas ......Page 177
9.2 The degenerate ideal Fermi gas (T < < T_F ) ......Page 179
9.3 Pauli paramagnetism ......Page 184
9.4 Landau diamagnetism ......Page 189
Exercises ......Page 195
10. Free Bosons: Bose-Einstein Condensation; Photon Gas ......Page 200
10.1 Bose-Einstein condensation ......Page 201
10.2 Photon gas. Planck statistics ......Page 212
Exercises ......Page 221
11.1 Crystalline phonons ......Page 224
11.2 Ferromagnetic magnons ......Page 233
11.3 Sketch of a theory of superfluidity ......Page 242
Exercises ......Page 245
12. Phase Transitions and Critical Phenomena: Classical Theories ......Page 248
12.1 Simple fluids. Van der Waals equation ......Page 249
12.2 The simple uniaxial ferromagnet. The Curie-Weiss equation ......Page 257
12.3 The Landau phenomenology ......Page 264
Exercises ......Page 267
13. The Ising Model ......Page 270
13.1 Exact solution in one dimension ......Page 273
13.2 Mean-field approximation for the Ising model ......Page 276
13.3 The Curie-Weiss model ......Page 279
13.4 The Bethe-Peierls approximation ......Page 281
13.5 Exact results on the square lattice ......Page 284
14.1 Scaling theory of the thermodynamic potentials ......Page 290
14.2 Scaling of the critical correlations ......Page 294
14.3 The Kadanoff construction ......Page 296
14.4 Renormalization of the ferromagnetic Ising chain ......Page 298
14.5 Renormalization of the Ising model on the square lattice ......Page 301
14.6 General scheme of application of the renormalization group ......Page 304
14.7 Renormalization group for the Ising ferromagnet on the triangular lattice ......Page 308
Exercises ......Page 314
15. Nonequilibrium Phenomena: I. Kinetic Methods ......Page 318
15.1 Boltzmann\'s kinetic method ......Page 319
15.2 The BBGKY hierarchy ......Page 331
Exercises ......Page 339
16. Nonequilibrlum phenomena: II. Stochastic Methods Stochastic Methods ......Page 344
16.1 Brownian motion. The Langevin equation ......Page 345
16.2 The Fokker-Planck equation ......Page 350
16.3 The master equation ......Page 353
16.4 The kinetic Ising model: Glauber\'s dynamics ......Page 357
16.5 The Monte Carlo method ......Page 365
Exercises ......Page 367
A.1 Stirling\'s asymptotic series ......Page 370
A.2 Gaussian integrals ......Page 372
A.3 Dirac\'s delta function ......Page 373
A.4 Volume of a hypersphere ......Page 375
A.5 Jacobian transformations ......Page 376
A.6 The saddle-point method ......Page 378
A.7 Numerical constants ......Page 381
Bibliography ......Page 384
Index ......Page 388