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A Topological Formula for Potts Lattice Gauge Theory Correlations
Abstract
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 applications we prove exponential decay of correlations between slowly growing Wilson loop variables for Ising lattice gauge theory on ℤ3 at all but the critical temperature, we demonstrate that the correlation length is finite at sufficiently high or low temperatures in any dimension, and we show that the correlation length of the model on ℤ4 with free boundary conditions equals that of the dual model with constant boundary conditions when q is prime.
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BibTeX
@misc{duncan2026topological,
title = {{A Topological Formula for Potts Lattice Gauge Theory Correlations}},
author = {Paul Duncan and Benjamin Schweinhart},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2607.02434},
eprint = {2607.02434},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.02434},
}
RIS
TY - UNPB
TI - A Topological Formula for Potts Lattice Gauge Theory Correlations
AU - Paul Duncan
AU - Benjamin Schweinhart
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2607.02434
UR - https://arxiv.org/abs/2607.02434
AB - 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 applications we prove exponential decay of correlations between slowly growing Wilson loop variables for Ising lattice gauge theory on ℤ^3 at all but the critical temperature, we demonstrate that the correlation length is finite at sufficiently high or low temperatures in any dimension, and we show that the correlation length of the model on ℤ^4 with free boundary conditions equals that of the dual model with constant boundary conditions when q is prime.
ER -