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. The scope of this book covers the basic theory for the graduate while it also reaches 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. They will also find it useful if they have some computer programming experience for example in Fortran. While percolation is treated as being 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 behaviour.