Correlated percolation unifying Ising, Potts, and bond percolation
The Fortuin-Kasteleyn random cluster model with parameters (p,q) unifies bond percolation (q=1), Ising model (q=2), and q-state Potts models. The weight of a configuration is p^|bonds| (1-p)^|missing| q^|clusters|. At q=2 on the square lattice, the critical point is p_c = √2/(1+√2) ≈ 0.586. Cluster correlations produce long-range spatial correlations absent in ordinary percolation.