## Upcoming Events

## GeorgeSquared Online Information Session

Dec 7, 2022, 12:00 - 1:00 PM

Virtual

## Women Leaders in STEM end of the semester social

Dec 8, 2022, 3:00 - 4:30 PM

Common area near 2200 in Exploratory Hall, Fairfax Campus

## MS Thesis Defense - Environmental Science and Policy

Dec 12, 2022, 2:00 - 4:00 PM

Virtual on Zoom

# Geometry MMA Seminar: The Plaquette Random Cluster Model and Potts Lattice Gauge Theory

Oct 24, 2022, 1:30 - 2:30 PM

**Speaker: **Benjamin Schweinhart, GMU

**Title: ** The Plaquette Random Cluster Model and Potts Lattice Gauge Theory

**Abstract:** The classical q-state Potts model of interacting spins in the integer lattice Zd – of which the Ising model is the special case q=2 – is one of the most important models in statistical physics and probability. It is often studied via a coupling with the Fortuin-Kasteleyn random cluster model of dependent bond percolation. In our talk, we describe how to generalize these models to higher-dimensional cubical complexes by defining q-state Potts lattice gauge theory and the plaquette random cluster model. When q is a prime integer, we show that the expectation of a Wilson loop variable in Potts lattice gauge theory (an analogue of its namesake in quantum field theory) equals the probability that the loop is null-homologous in the corresponding plaquette random cluster model. We also prove that the i-dimensional plaquette random cluster model in the 2i-dimensional torus exhibits a sharp phase transition in the sense of homological percolation: that is, the emergence of giant cycles which are non-trivial homology classes in the ambient torus.

**Time:** Monday, October 24, 2022 – 1:30pm-2:30pm

**Place:** Exploratory Hall, Room 4208