This text provides a thoroughly modern graduate-level introduction to the theory of critical behaviour. 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 behaviour, finite-size scaling, perturbative renormalization methods, low-dimensional systems, surface critical behaviour, 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 other 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
This is an advanced 1997 text for first-year graduate students in physics and engineering taking a standard classical mechanics course. It was the first book to describe the subject in the context of the language and methods of modern nonlinear dynamics. The organising principle of the text is integrability vs. nonintegrability. Flows in phase space and transformations are introduced early and systematically and are applied throughout the text. The standard integrable problems of elementary physics are analysed from the standpoint of flows, transformations, and integrability. This approach then allows the author to introduce most of the interesting ideas of modern nonlinear dynamics via the most elementary nonintegrable problems of Newtonian mechanics. This text will be of value to physicists and engineers taking graduate courses in classical mechanics. It will also interest specialists in nonlinear dynamics, mathematicians, engineers and system theorists.
This is an advanced 1997 text for first-year graduate students in physics and engineering taking a standard classical mechanics course. It was the first book to describe the subject in the context of the language and methods of modern nonlinear dynamics. The organising principle of the text is integrability vs. nonintegrability. Flows in phase space and transformations are introduced early and systematically and are applied throughout the text. The standard integrable problems of elementary physics are analysed from the standpoint of flows, transformations, and integrability. This approach then allows the author to introduce most of the interesting ideas of modern nonlinear dynamics via the most elementary nonintegrable problems of Newtonian mechanics. This text will be of value to physicists and engineers taking graduate courses in classical mechanics. It will also interest specialists in nonlinear dynamics, mathematicians, engineers and system theorists.