On the Random Cluster Model

The Random Cluster Model offers an interesting reformulation of the Ising and Potts Models in the language of percolation theory. In one regime, the model obeys Positive Association, which has broad implications. Another prominent property of the Random Cluster Model is the existence of a critical point, separating two phases with and without infinite clusters, however much is still unknown or unproven about this critical point. The central results in Random Cluster Theory toward definition and proof of the existence of the critical point are presented. Monte-Carlo simulations are then used to computationally test the critical behavior of the model, and support a conjecture about the behavior of the critical point on the square lattice