We prove that Wilson loop expectations in (d-2)-dimensional Potts lattice gauge theory on Zd undergo a sharp phase transition from an area law to a perimeter law. The foundation of our proof strategy is the generalization of the random cluster model and its coupling with the Potts model to higher dimensions. This results in a cell complex representation of Potts lattice gauge theory for which a Wilson loop expectation equals the probability that the loop is “bounded by a surface of plaquettes” in a sense made precise by homology theory. This is joint work with Paul Duncan.
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