Introduction To Percolation Theory

Percolation theory deals with clustering, criticality, diffusion, fractals, phase transitions and disordered systems. It provides a quantitative model for understanding these phenomena, and therefore provides a theoretical, statistical background to many physical and natural science disciplines. This book explains the basic theory for the graduate while also reaching into the specialized fields of disordered systems and renormalization groups. Readers are expected to be able to handle some fundamental mathematical procedures, such as integration and differentiation of single variable functions, probability and statistics. Computer programming experience in Fortran is also useful. While percolation is treated as a fundamentally physical concept, its relevance to various natural and living systems is addressed. Much of the book deals with systems lying close to the critical point phase transition point, where the subject is at its most interesting and sensitive. This book should be of value to all those who deal with systems which exhibit critical points and phase transition behavior.