×

zbMATH — the first resource for mathematics

Statistical mechanics. 2nd ed. (English) Zbl 0862.00007
Oxford: Butterworth Heinemann. xiv, 529 p. (1996).
[The first ed. (1972) was not reviewed]
The book is devoted to postgraduate courses in statistical mechanics. It consists of fourteen chapters and a number of mathematical appendices. The first four chapters are concerned with the main notions and techniques of equilibrium statistical mechanics of classical as well as quantum systems of distinguishable entities. They contain a brief but nice discussion of the foundations of equilibrium statistical physics and introduce basic notions of microcanonical, canonical and grand canonical ensembles. Chapter 5 treats indistinguishable entities. With this chapter the equipment is completed which allows to study simple physical systems. In Chapters 6-8 ideal gases are studied in great detail. Many particular topics are included: Pauli paramagnetism, Landau diamagnetism, thermionic emission, photoelectric emission, physics of white dwarfs.
The following two chapters are devoted to statistical mechanics of interacting systems. Two basic methods are presented: the cluster expansion and second quantization. The elements of the theory of Fermi and Bose liquids are given.
In Chapters 11-13 the theory of phase transitions is sketched. First, in Chapter 11 some basic notions (critical exponents, thermodynamic inequalities, scaling hypothesis) are introduced. The ideas of mean-field approximation (Bragg-Williams approximation) and Bethe approximation are explained. In Chapter 12 exactly solvable models are reviewed: Ising model in one and two dimensions, spherical model and ideal Bose gas in \(n\) dimensions. The renormalization group approach is sketched in Chapter 13. It is of course impossible to give a full account of the subject in a short chapter. The discussion is therefore very brief but the main points are well-emphasized. It would be advantagous if the author included the renormalization group treatment of the one-dimensional Ising model in a complex extremal magnetic field. This model, although somewhat unphysical, exhibits surprisingly rich renormalization group behaviour, including chaotic trajectories.
The last chapter is devoted to fluctuations. “Classical” topics are treated, thermodynamic theory of fluctuations, Brownian motion according to Einstein, Smoluchowski and Langevin, Fokker-Planck equation, fluctuation-dissipation theorem and Onsager relations.
Even chapter includes a number of interesting and carefully selected exercises.
In summary, the book provides a very clear exposition of the main ideas and techniques of statistical physics.

MSC:
00A79 Physics (Use more specific entries from Sections 70-XX through 86-XX when possible)
82-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistical mechanics
82Bxx Equilibrium statistical mechanics
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B05 Classical equilibrium statistical mechanics (general)
82B10 Quantum equilibrium statistical mechanics (general)
82B28 Renormalization group methods in equilibrium statistical mechanics
PDF BibTeX XML Cite