The Plaquette Random Cluster Model and Potts Lattice Gauge Theory

Explore a conference talk on the Plaquette Random Cluster Model and Potts Lattice Gauge Theory presented by Benjamin Schweinhart from George Mason University. Delve into the proof of a sharp phase transition in Wilson loop expectations within (d-2)-dimensional Potts lattice gauge theory on Zd, transitioning from an area law to a perimeter law. Discover how the random cluster model and its coupling with the Potts model are generalized to higher dimensions, resulting in a cell complex representation of Potts lattice gauge theory. Understand how this representation allows Wilson loop expectations to be interpreted as probabilities of loops being "bounded by a surface of plaquettes," a concept clarified through homology theory. Gain insights into this collaborative research with Paul Duncan, presented at IPAM's Statistical Mechanics Beyond 2D Workshop.