Percolation theory

Abstract

The theory or percolation models is developed following general ideas in the area of critical phenomena. The review is an exposition of current phase transition theory in a geometrical context. As such, it includes a discussion of scaling relations between critical exponents and their calculation using series expansion methods. Renormalisation group techniques are also considered. The major difference between percolation and other phase transition models is the absence of a Hamiltonian. Instead, the theory is based entirely on probabilistic arguments. A discussion of the connections with classical probability theory is also given.