Recorded 07 May 2024. Benjamin Schweinhart of George Mason University presents "The Plaquette Random Cluster Model and Potts Lattice Gauge Theory" at IPAM's Statistical Mechanics Beyond 2D Workshop. Abstract: 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. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-iii-statistical-mechanics-beyond-2d/