Scaling Properties, Fractals, and the Renormalization Group Approach to Percolation

Definition of the Subject

Percolation theory mostly deals with large lattices where every site is randomly either occupied or empty. In particular it studies the resultingclusters which are sets of neighboring occupied sites.

Introduction

Paul Flory , who later got the Chemistry Nobel prize, published in 1941 the first percolation theory [1], to describe the vulcanization of rubber [2]. Others laterapplied and generalized it, in particular by dealing with percolation theory on lattices and by studying it with computers. Most of the theory presentedhere was known around 1980, though in the case of computer simulation with less accuracy than today. But on the questions of universality, of criticalspanning probability and of the uniqueness of infinite clusters, the 1990's have shown some of our earlier opinions to be wrong. And even today it isquestioned by some that the critical exponents of percolation theory can be applied to real polymer gelation , the application which...