Renormalization Methods: Critical Phenomena, Chaos, Fractal Structures

Renormalization analysis reveals how microscopic mechanisms can organize themselves to produce macroscopic consequences. These techniques are applied in various fields of physics, from phase transitions and magnetic systems, to dynamical systems, percolation and fractal structures, random walks, and polymers.
Originally conceived some thirty years ago in the context of quantum electrodynamics, renormalization methods have progressively developed into an indispensable analytical tool used in widely varying domains of physics and applied mathematics, such as aeo phase transitions and critical phenomena aeo dynamical systems and chaos aeo developed turbulence aeo fractal structures and complex systems aeo percolation aeo polymer physics aeo diffusion in disordered media aeo measure theory and stochastic processes. By explaining the fundamental principles of renormalization theory such as scale invariance and universality which lie behind all the technical variations, this book aims to guide the reader to a more unified understanding of today s physics. The book is based on a very accessible main text, supplemented by several more specialized sections; it is intended for graduate students and for researchers who are seeking an introduction to a new area of electrodynamics or a general overview of the physical phenomena to which renormalization methods are applied.