Fortuin-Kasteleyn Random Cluster Model
Unifying percolation (q=1), Ising (q=2), and Potts models via the FK representation
Controls
Bond probability p:
0.5
Cluster weight q:
2
Grid size L:
30
Regenerate
FK weight:
w(G) = p^|E| (1-p)^(|E̅|) q^k(G)
k(G) = number of connected clusters
q=1: bond percolation
q=2: Ising model (β = atanh(p/q^0.5))
q=3,4: 3- and 4-state Potts
Critical p_c(q) = √q/(1+√q) on ℤ²