Critical phenomena is one of the most exciting areas of modern physics. This 2007 book provides a thorough but economic introduction into the principles and techniques of the theory of critical phenomena and the renormalization group, from the perspective of modern condensed matter physics. Assuming basic knowledge of quantum and statistical mechanics, the book discusses phase transitions in magnets, superfluids, superconductors, and gauge field theories. Particular attention is given to topics such as gauge field fluctuations in superconductors, the Kosterlitz-Thouless transition, duality transformations, and quantum phase transitions - all of which are at the forefront of physics research. This book contains numerous problems of varying degrees of difficulty, with solutions. These problems provide readers with a wealth of material to test their understanding of the subject. It is ideal for graduate students and more experienced researchers in the fields of condensed matter physics, statistical physics, and many-body physics.
Igor Herbut is Professor of Physics at Simon Fraser University in Burnaby, British Columbia. He has held visiting appointments at Max Planck Institute, Kavli Institute for Theoretical Physics, and Tokyo Institute of Technology. Professor Herbut has authored a number of research papers on quantum phase transitions, disordered systems, gauge field theories, and high-temperature superconductivity.
Preface; 1. Introduction; 2. Ginzburg-Landau-Wilson theory; 3. Renormalization group; 4. Superconducting transition; 5. Near lower critical dimension; 6. Kosterlitz-Thouless transition; 7. Duality in higher dimensions; 8. Quantum phase transitions; Appendix A. Hubbard-Stratonovich transformation; Appendix B. Linked-cluster theorem; Appendix C. Gauge fixing for long-range order; Select bibliography; Index.