Simulation methods are providing considerable excitement in theoretical physics as a bridge between theory and experiment. To treat complex systems analytically invariably requires approximations. Computer simulations can go beyond the analytical results and provide insights into the physical behavior underlying the experimental data.
The Preface to this book states that its goal is “to present a selection of fundamental techniques that are now being widely applied in many areas of physics, mathematics, chemistry and biology.” The book “does not and cannot give a complete introduction to simulational physics.” Even such modest goals are hardly met by this book.
The first chapter provides an intriguing introduction through the percolation problem, with a simple 10-line FORTRAN routine doing the work. Unfortunately, this interesting, clear example is the last in the book. Chapter 2 (General Introduction to Computer Simulation Methods) immediately drops the reader into Hamiltonians, distribution functions, ensemble averages, and partition functions.
Chapter 3 is devoted to Deterministic Methods. A taste of the coverage is given by noting that the first example treated is a simulation of 256 argon atoms in a face-centered cubic lattice interacting according to a Lennard-Jones potential. Even noting the complexity of the example, the treatment is hardly textbook level. Terms are used without explanation (e.g., “minimum image convention”), and approaches are stated without clarification (e.g., “To ensure a reasonable numerical stability the basic time increment is taken to be h = 0.064 or 2*10−14s.”). Also, an “ad hoc readjustment of the velocities” is used without any real explanation of why it is required. Lastly, although the results of the simulation are plotted in some detail, no argon data are presented for comparison. Unfortunately, all eight examples in the book follow these trends.
Chapter 4, entitled Stochastic Methods, covers Markov Processes (Brownian Dynamics) and Monte Carlo Methods (the Ising Model, treated in the microcanonical, canonical, and grand ensembles).
Appendix 2 contains FORTRAN source listings used in the examples. However, the transition from the text to the code is not particularly clear. The code lacks detailed comments and the benefit of subroutines.
The book is poorly produced. The output from a word processor has been reduced and printed. The equations, in particular, are hard to read. The text also contains many spelling and typographical errors.
The book is aimed at seniors and first-year graduate students. However, a very thorough background in the theoretical aspects of statistical mechanics is a prerequisite for this book. The author cites references as a substitute for explanations, and the complete, detailed exposition one expects from a textbook is missing. The problems, which are mostly extensions of the text, are dull. Ultimately, the book fails to convey the diversity, enthusiasm, and value of simulation methods.
