Fortuin–Kasteleyn random cluster model

Summary

The random cluster model is a probability measure on sets of edges of a graph with two parameters $p$ and $q$. It weights each edge set by the usual percolation weight times $q$ to the number of connected components. For $q = 1$ it is Bernoulli bond percolation, and for integer $q \ge 2$ it is coupled with the $q$-state Potts model. This puts percolation, the Ising model and the Potts models into one family and gives geometric tools for their phase transitions.