Interfaces for random cluster models (Q1871888)

The authors construct a Gibbs measure for a random cluster model on \(\mathbb{Z}^d\) which is not translationally invariant for \(d\geq 3\), the critical occupation probability \(p_c\) and sufficiently large \(q\). It is realized as a limit of the measures in finite boxes with the boundary conditions: occupied in the upper halfspace and vacant in the lower halfspace. For the limit measure there is a rigid interface separating an infinite occupied cluster in the upper halfspace from the region with only finite clusters in the lower halfspace.