It is known that the random cluster model with $q = 1$ corresponds to bond percolation, and $q = 2, 3, ... $ corresponds to the $q$-state Potts model. Both of these have a local description.
What about a random cluster model with non-integer $q$?
I think the answer is no, and I suppose there is a way to see this by computing certain correlations. Does anyone know a proof?
