A family of Probabilistic models invented by Fortuin and Kasteleyn which include Percolation, and the Ising and Potts models as special cases.

The configuration space of the random-cluster model is the set of all subsets of the edge-set $E$, which we represent as the set $\Omega={0,1}^E$. The model may be viewed asa parametric family of probability measures $\phi_{p,q}$ on $\Omega$. When $q=1$, we recover bond Percolation, when $q=2$, we have the Ising model, and when $q=2,3,4,...$ we have different versions of the Potts model.

It turns out that long-range order in a Potts model corresponds to theexistence of infinite clusters in the corresponding random-cluster model. In this sense the Potts and percolation phase transitions are counterparts of one another.

Reference: Grimmet - The Random-Cluster Model