Condensed Matter Physics Michael P. Marder Wiley, New York, 2000. $94.95 (895 pp.). ISBN 0-471-17779-2
A satisfactory general-purpose text book for a graduate course on condensed matter physics is difficult to find. The venerable old books that do a great job on the basics fail to capture the excitement and advances of the last quarter-century. The more recent books tend to be rather specialized or emphasize a particular point of view.
The problem is fundamental: The field overlaps classical physics, crystallography, quantum mechanics, statistical mechanics, fluid dynamics, and materials physics. For more advanced topics, one needs quantum field theory and sophisticated mathematics. In recent years, competition has developed between rather simple models that convey the basic principles and more rigorous derivations that allow “first-principles” calculations of properties. How does one pull it all together into a coherent whole?
Michael Marder’s new book, Condensed Matter Physics , is a valiant attempt to tame the devil. The book’s ambition is to cover the basics with a modern flavor while retaining a historical perspective, give a feel for experimental and computational methods, cover many of the exciting new developments, and go beyond the traditional “crystal physics” to complex materials, fluids, and hybrid forms of condensed matter. Has he succeeded? My answer is that he did a very good job, but there are some shortcomings that can, at least to some extent, be improved in a second edition.
The book gives a good account of the now-classical “crystal physics” that is the heart and soul of the venerable old books. It also gives a panoramic view, however, of the diversity of modern condensed matter physics by covering surfaces and scanning tunneling microscopy, interfaces, the quantum and fractional Hall effects, giant magnetoresistance, quantum dots, high-temperature superconductivity, and critical phenomena. The book also provides a credible account of polymers and fluids, dislocations and cracks, plasticity, alloys, and liquid crystals, and it does not shy away from transistors. For the most part, Marder gives what one might call an “initial account” of these diverse topics, enriching students without taxing them with advanced formulations.
Marder also does an excellent job of outlining the mainstream experimental methods that are used to measure the various properties. This is an important element for a textbook aimed at a mix of students who will pursue either experimental or theoretical research. In addition, he gives introductory glimpses of computation, which is emerging as a third, distinct mode of research. He also mentions some of the challenges faced by the pioneers in the field and places them in their historical context. These descriptions are both enriching and unobtrusive, as he carefully avoids getting dragged into the historical evolution of the field. The book also contains a collection of tables that give a sense of reality and provide a handy reference. The problem sets are substantial and a solutions manual is being compiled to make the teacher’s life a bit easier.
Marder made a good effort to avoid one of the major sins of most books with similar objectives: He goes to great lengths to tell you where all the equations come from; the use of tiny print next to equations often tells you where you can find derivations. He still falls into the trap here and there, however. For example, in the section on phase separations, he mentions Fick’s law of diffusion without any indication of where it comes from or where one can find a derivation. Clearly, problems of this kind can be fixed in a second edition.
One weakness that may be hard to fix is the emphasis on rather disconnected models, a practice that does not convey the underlying unity of the field and does not reveal the connections to corresponding computational methods. My point is best exemplified by the chapters on electronic structure. They first cover “free-electron” bands, the periodic crystal potential and the Bloch theorem, and nearly-free-electron bands. A subsequent chapter starts with the Born–Oppenheimer approximation, the many-electron problem, Hartree–Fock, and density functional theory. I would much rather do it in reverse: show how density functional theory rigorously yields an effective one-electron potential, introduce the Bloch theorem, and then describe the range of solutions from free to nearly-free to real electrons and realistic computations. Similar comments apply to a few other topics.
In summary, the main strength of the book is that it conveys the enormous breadth of modern condensed matter physics and gives a basic, often conceptual account of these diverse topics. But the exposition tends to be fragmented and does not capture underlying unifying themes.
