The Theory of Critical Phenomena: An Introduction to the Renormalization Group (Oxford Science Publications)

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The successful calculation of critical exponents for continuous phase transitions is one of the main achievements of theoretical physics over the last quarter-century. This was achieved through the use of scaling and field-theoretic techniques which have since become standard equipment in many areas of physics, especially quantum field theory. This book provides a thorough introduction to these techniques. Continuous phase transitions are introduced, then the necessary statistical mechanics is summarized, followed by standard models, some exact solutions and techniques for numerical simulations. The real-space renormalization group and mean-field theory are then explained and illustrated. The final chapters cover the Landau-Ginzburg model, from physical motivation, through diagrammatic perturbation theory and renormalization to therenormalization group and the calculation of critical exponents above and below the critical temperature.

The Theory of Critical Phenomena: An Introduction to the Renormalization Group (Oxford Science Publications) Review

This is a highly pedagogical book on the theory of critical phenomena and the renormalization group (RG). Field-theoretic methods are introduced gradually, and the physics is always illustrated with well-chosen examples. Technical details are explained thoroughlly and oftentimes summarized in ``boxes'' which span most of the book. At the end of every chapter, a set of problems allows the reader to test his/her understanding of the subject matter, and solutions to the problems are provided at the end of the book. Two regrets though: (i) that the authors did not touch at all the (less rigorous) but highly intuitive and widely used momentum shell renormalization group technique; and (ii) that the treatment of two-dimensional systems and the Kosterlitz thouless transition is a little superficial. Apart from that, this book is just great. A very useful book.

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