  In the Ising and Potts model, random cluster representations provide a
geometric interpretation to spin correlations. We discuss similar constructions
for the Villain and XY models, where spins take values in the circle, as well
as extensions to models with different single site spin spaces. In the Villain
case, we highlight natural interpretation in terms of the cable system
extension of the model. We also list questions and open problems on the cluster
representations obtained in this fashion.
