Phase Transition - Characteristic Properties - Percolation Theory

Percolation Theory

Another phenomenon which shows phase transitions and critical exponents is percolation. The simplest example is perhaps percolation in a two dimensional square lattice. Sites are randomly occupied with probability p. For small values of p the occupied sites form only small clusters. At a certain threshold p_c a giant cluster is formed and we have a second order phase transition. The behavior of P_∞ near p_c is, P_∞~(p-p_c)β, where β is a critical exponent.