Statistical Mechanics and Applications in Condensed Matter, Carlo Di Castro and Roberto Raimondi, Cambridge U. Press, 2015. $79.99 (544 pp.). ISBN 978-1-107-03940-7 Buy at Amazon
Science educators and students alike have long struggled to answer the question, “What textbooks will help me learn that?” In condensed-matter theory, the problem is aggravated by the fast and turbulent growth of new, exotic subjects, whose substance, meaning, and connection to the standard theories enshrined in venerable texts are often unclear to the unsavvy.
Carlo Di Castro and Roberto Raimondi’s Statistical Mechanics and Applications in Condensed Matter answers the question and effectively fills a good part of the theory gap in conventional texts for the lively area of research that involves condensed-matter physics, many-body theory, and quantum statistical mechanics. The authors, whose competence is beyond doubt, employ a well-considered approach to bridge background statistical mechanics topics, standard condensed-matter physics applications, and a limited but inspiring choice of advanced and timely many-body themes.
The first seven chapters offer a self-contained presentation of introductory statistical mechanics, both classical and quantum, starting from basic thermodynamics. In subsequent chapters, readers with a particular interest in phase transitions and equilibrium critical phenomena can learn about such approaches as mean-field theory, Landau theory, scaling, and the renormalization group. The authors deliver a well-designed exposition of quantum many-body phenomena before moving on to explanations of superconductivity, superfluidity, and the general properties of Fermi liquids. That exposition prepares the reader for the ensuing discussion of such advanced topics as the microscopic foundations of Fermi liquids, the Tomonaga–Luttinger model for one-dimensional systems, Anderson localization, and weak-localization phenomena. Compact yet effective presentations of thermal Green’s function diagrams and Feynman diagrams— traditional tools of the many-body theorist—are applied to modern and advanced aspects of condensed-matter theory, in particular, to interactions in disordered fermionic systems.
The authors acknowledge making a deliberate choice not to include everything that is new, or hot, or even important, such as the quantum Hall effect, or some of the wonders of Mott physics, noise physics, and topological insulators. Indeed, those subjects are already well covered in recent books and reviews. However, Di Castro and Raimondi do present some recent developments that are rarely found in course texts. For instance, their treatment of the fluctuation-dissipation theorem goes well beyond explaining the Crooks relationship and the Jarzynski inequality. Another example is their discussion of the diagrammatic aspects of the Tomonaga‒Luttinger model and Ward identities.
Whatever subjects the authors include, they cover in depth. They avoid the temptation to simply announce results in words or to show results and equations without including the mathematical proof. Instead, they provide an abundance of proofs to go along with appropriate verbal explanations. They take great care to relate detailed results to the fundamentals and even include historical facts that are rarely covered in technical books and articles.
The book’s end-of-chapter problems deserve special mention. They are relatively few in number, but are well designed; some of them are quite demanding and could be considered as small projects. Such problems are a rare gift: Students that engage with the exercises, whose solutions can be found in an appendix, will greatly benefit in their understanding. Lecturers will benefit, too: The poor souls are often at a loss on where to find good problems.
In sum, Statistical Mechanics and Applications in Condensed Matter is a well-designed, user-friendly text that represents an impressive and successful effort to synthesize modern aspects of condensed-matter and many-body phenomena. I have no doubt that this book will soon be found—and deservedly so—in physics libraries and on the bookshelves of many students and researchers.
Erio Tosatti is an emeritus professor of physics at the International School for Advanced Studies (SISSA) and founder and senior collaborator of the condensed-matter theory group at the Abdus Salam International Centre for Theoretical Physics. Both institutions are in Trieste, Italy. Consultation with Prof. Giuseppe Santoro of SISSA is gratefully acknowledged.
