 Random-cluster boundary condition

A boundary condition for a finite-box random-cluster measure is a partition of the boundary vertices. All vertices in one block are identified before counting open components; the identifications carry no Bernoulli edge factors. The weight is $p^{o(\omega )}(1-p{)}^{|E|-o(\omega )}{q}^{k_{\xi }(\omega )}$. A coarser partition makes more identifications. General partitions need not have a planar realization.