The Field Theoretic Renormalization Group in Critical Behavior Theory and Stochastic Dynamics (PDF)

Although the renormalization-group (RG) technique was first developed in quantum field theory in the 1950s, it later became clear that the method is equally applicable to classical problems involving random fields. It is, in fact, the simplest and most effective method for establishing scaling in specific models and calculating the corresponding critical exponents.

This book presents a detailed exposition of the quantum field RG technique and its applications to various problems in the classical theory of critical behavior and stochastic dynamics. This most formal and technically effective version of the technique is based on the well-developed techniques of ultraviolet renormalization, which provides a reliable foundation for the quantum field version of the RG. This treatment focuses primarily on providing an in-depth description of the computation techniques. Using examples of particular calculations, the author gives as many details as possible and presents the final results in universal notation with the highest level of accuracy presently attained.

From problems in critical statics and dynamics to problems in the theory of polymers, the stochastic theory of turbulence, and random diffusion, the list of applications continues to grow, and an acquaintance with the RG technique has become an essential element of the modern theoretical physicist's education. Self-contained, clearly written, and well organized, this book forms an outstanding reference for graduate students and researchers in theoretical physics, applied mathematics, statistical physics, and fluid dynamics.