L. Peliti: Statistical Mechanics in a Nutshell

Abstract

Drawing from his considerable involvement as a researcher in the field, and from his teaching notes on the subject for over 15 years, Luca Peliti had put together a remarkably selfcontained and comprehensive, introductory textbook, Appunti di Meccanica Statistica (Bollati Boringhieri 2003). The recent English translation, “Statistical Mechanics in a Nutshell” (by Mark Epstein, from the original Italian), fits very nicely in the new In a Nutshell Princeton series, conceived to provide “concise, accessible, and up-to-date textbooks for advanced undergraduate and graduate students on key subjects in the physical sciences.” The book is in fact almost more of a reference book than a traditional textbook. Though limited to the putative syllabus for a course in statistical mechanics, it is exceptionally comprehensive in scope. Following a brief motivational introduction, utilizing the example of an ideal gas, in Chap. 1, classical thermodynamics is broadly reviewed, in Chap. 2, including the more obscure thermodynamic potentials related to particle number, and the useful Koenig-Born diagram trick for quickly deriving all pertinent Maxwell relations. The statistical mechanical approach, the partition function for different probability ensembles, and the basic application of this machinery to interaction-free systems of Bosons and Fermions is expounded upon in Chaps. 3 and 4. Chapter 5 looks at the liquid-gas transition, as described by the Van der Waals equation and the lattice gas (or Ising) model, and uses this example for the introduction of basic concepts such as critical exponents, universality, and scaling, as well as techniques, including mean-field and Landau theory, and culminating with an exact solution of the 2-dimensional Ising model. These first five chapters comprise the standard material found in many other textbooks on the subject, though none equals the present book in its thoroughness and scope. Chapter 6 discusses renormalization group theory, reviewing all the major techniques and approaches. The theory of classical fluids and the virial expansion (sometimes included in other texts) is covered in Chap. 7. Chapter 8 introduces numerical simulations, molecular dynamics and the Monte Carlo method. Brownian and Generalized Brownian motion is discussed in Chap. 9, and is used to introduce