An introduction to percolation theory

Percolation theory, the theory of the properties of classical particles interacting with a random medium, is of wide applicability and provides a simple picture exhibiting critical behaviour, the features of which are well understood and amenable to detailed calculation. In this review the concepts of percolation theory and the general features associated with the critical region about the onset of percolation are developed in detail. In particular, several dimensional invariants are examined which make it possible to unify much of the available information, and to extend the insights of percolation theory to processes which have not yet received numerical study. The compilation of the results of percolation theory, both exact and numerical, is believed to be complete through 1970. A selective bibliography is given. In a concluding chapter several recent applications of percolation theory to classical and to quantum mechanical problems are discussed.