Physics of Critical Fluctuations

Building on Wilson's renormalization group, the authors have developed a unified approach that not only reproduces known results but also yields new results. A systematic exposition of the contemporary theory of phase transitions, the book includes detailed discussions of phenomena in Heisenberg magnets, granular super-conducting alloys, anisotropic systems of dipoles, and liquid-vapor transitions. Suitable for advanced undergraduates as well as graduate students in physics, the text assumes some knowledge of statistical mechanics, but is otherwise self-contained.

Theoretical and experimental studies of phase transitions are at the forefront of modern condensed-matter physics. The seminal insight into the role played by fluctuations led to the renormalization group, an approach that has proved extremely useful in many other fields as well. This text considers a wide variety of problems in the theory of phase transitions, revealing their common features as well as their distinctions. Formal aspects are developed as required in discussions of particular systems, and theory is compared to experiment wherever possible. This book begins with a review of the classical approach, including the main aspects of a self-consistent treatment of systems with broken symmetry and a discussion of the Ginzburg-Landau functional. It then turns to a treatment of the renormalization group, discussing both Wilson's formulation based on Kadanoff's scale invariance as well as the approach using field theory. The authors then turn to a generalized approach using scale equations, which eliminates many of the problems of the other formulations. Subsequent chapters discuss applications of this approach: first to simple models; then to more realistic systems such as complex Heisenberg magnets, antiferromagnets, ferroelectrics, impure systems, and high-T(subscript c) superconductors. Finally, in the last two chapters many of these systems are analyzed within the framework of exactly solvable models. Suitable for advanced undergraduates as well as graduate students in physics, the text assumes some knowledge of statistical mechanics, but is otherwise self-contained.