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 pc a giant cluster is formed and we have a second order phase transition. The behavior of P near pc is, P~(p-pc)β, where β is a critical exponent.

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