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.
The Plaquette Random Cluster Model and Potts Lattice Gauge Theory
Institute for Pure & Applied Mathematics (IPAM) via YouTube
Overview
Syllabus
Benjamin Schweinhart - The Plaquette Random Cluster Model and Potts Lattice Gauge Theory
Taught by
Institute for Pure & Applied Mathematics (IPAM)