**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.

Read more about this topic: Phase Changes, Characteristic Properties

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“Frankly, these days, without a *theory* to go with it, I can’t see a painting.”

—Tom Wolfe (b. 1931)