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

Here is a much-needed basic text that covers a vital area in physics for beginning graduate students. 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, one that assumes only a sound undergraduate background in physics and mathematics. 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 next explained and illustrated. The last eight chapters cover the Landau-Ginzburg model, from physical motivation, through diagrammatic perturbation theory and renormalization to the renormalization group and the calculation of critical exponents above and below the critical temperature.