Although chemistry is primarily concerned with molecules and mechanisms, the properties of bulk matter are also an important, but less appreciated, part of the science. All chemists receive an introduction to thermodynamics and statistical mechanics, the primary tools for the understanding of bulk matter, but rarely does that introduction explore the simple but profound questions such as why is bulk matter stable? and, how can we understand a phase transition? Answers to these questions require a deep understanding of the theoretical models for bulk matter and the often sophisticated mathematical techniques required to analyze them. This is the formidable task that Martin Krieger sets for himself in Constitutions of Matter.

Perhaps the central question of statistical mechanics is what makes a thermodynamic description of matter possible - how do the myriad of molecular variables reduce to the small number of experimentally accessible quantities used in macroscopic theory. This is the first issue discussed by Krieger, who shows how the mathematical analysis of models of matter yields important insights into the way scientists understand the world. In parallel he considers the question of the stability of bulk matter, beginning with the stability of atoms, proceeding to the crucial role of Fermi-Dirac statistics in the stability of bulk phases, and ending with a discussion of the importance of screening for the existence of a thermodynamic description. Finally, the development of the modern theory of phase transitions is discussed in detail, focusing particularly on Onsager's solution of the two-dimensional Ising model and subsequent theoretical advances.

Throughout the book, Krieger emphasizes the role of mathematics in understanding the physical world. What seem to be mathematical tricks actually carry physical and philosophical meaning. Studying models is one way that scientists, in Krieger's phrase, "take hold of the world". A new solution to an old problem provides new insights into the important physical mechanisms. Constitutions of Matter is an extended study of how mathematical physics has resulted in a profound understanding of an everyday phenomenon, the stability of bulk matter. In addition, it is a review of some of the most important results in statistical mechanics of the past 50 years.

In the preface Krieger suggests that, if read selectively, the book is accessible to lay readers as well as professional physicists and chemists. As someone who has spent 25 years working in statistical mechanics, I think he has rather overestimated the lay reader. Chemists with a good background in thermodynamics and statistical mechanics and who are interested either in an interesting philosophical perspective on mathematical physics or a better understanding of the modern theory of bulk matter and phase transitions will find this book valuable. It requires sustained effort, but the rewards in terms of a deeper insight into both statistical mechanics and the nature of bulk matter are considerable.

Jeffrey Kovac
Department of Chemistry
University of Tennessee
Knoxville, TN 37996-1600