Some Properties of the Plaquette Random-Cluster Model

Abstract

We show that the $i$-dimensional plaqutte random-cluster model with coefficients in ${\mathbb{Z}}_q$ is dual to a $(d-i)$-dimensional plaquette random cluster model. In addition, we explore boundary conditions, infinite volume limits, and uniqueness for these models. For previously known results, we provide new proofs that rely more on the tools of algebraic topology.

Fixed typos