7 papers · 1 filter
A Topological Formula for Potts Lattice Gauge Theory Correlations
Paul Duncan, Benjamin Schweinhart
We exhibit a formula relating the correlation between Wilson loop variables in Potts lattice gauge theory to a topological quantity in the plaquette random cluster model. As applic…
Voronoi Percolation: Topological Stability and Giant Cycles
Benjamin Schweinhart, Morgan Shuman
We study the topological stability of Voronoi percolation in higher dimensions. We show that slightly increasing p allows a discretization that preserves increasing topological pro…
A Cellular Representation of the Potts Lattice Higgs Model
Summer Eldridge, Malin P. Forsström, Benjamin Schweinhart
The -dimensional Potts lattice Higgs model is a random assignment of spins in to the -dimensional cells of a cell complex induced by a Hamiltonian with a Potts…
Disks, Surfaces, and Entanglement Percolation
Paul Duncan, Benjamin Schweinhart, David Sivakoff
We study the probability that a loop is null-homotopic -- that is, bounded by the continuous image of a disk -- in plaquette percolation on Locally, the event that…
On the Continuity of Enhancement Percolation
Paul Duncan, Benjamin Schweinhart, David Sivakoff
We study bond percolation in with an unbounded family of enhancements that enable additional bonds to act as open. A natural question is whether percolation occurs i…
Some Properties of the Plaquette Random-Cluster Model
Paul Duncan, Benjamin Schweinhart
We show that the -dimensional plaqutte random-cluster model with coefficients in is dual to a -dimensional plaquette random cluster model. In addition, we…