Scaling and Renormalization in Statistical Physics

This text provides a thoroughly modern graduate-level introduction to the theory of critical behavior. Beginning with a brief review of phase transitions in simple systems and of mean field theory the text then goes on to introduce the core ideas of the renormalization group. Following chapters cover phase diagrams fixed points cross-over behavior finite-size scaling perturbative renormalization methods low-dimensional systems surface critical behavior random systems percolation polymer statistics critical dynamics and conformal symmetry. The book closes with an appendix on Gaussian integration a selected bibliography and a detailed index. Many problems are included. The emphasis throughout is on providing an elementary and intuitive approach. In particular the perturbative method introduced leads among applications to a simple derivation of the epsilon expansion in which all the actual calculations (at least to lowest order) reduce to simple counting avoiding the need for Feynman diagrams.