A Sharp Deconfinement Transition for Potts Lattice Gauge Theory in Codimension Two
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913340583837696 |
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| author | Duncan, Paul Schweinhart, Benjamin |
| author_facet | Duncan, Paul Schweinhart, Benjamin |
| contents | In 1983, Aizenman, Chayes, Chayes, Fröhlich, and Russo proved that $2$-dimensional Bernoulli plaquette percolation in $\mathbb{Z}^3$ exhibits a sharp phase transition for the event that a large rectangular loop is "bounded by a surface of plaquettes.'' We extend this result both to $(d-1)$-dimensional plaquette percolation in $\mathbb{Z}^d,$ and to a dependent model of plaquette percolation called the plaquette random-cluster model. As a consequence, we obtain a sharp phase transition for Wilson loop expectations in $(d-2)$-dimensional $q$-state Potts hyperlattice gauge theory on $\mathbb{Z}^d$ dual to that of the Potts model. Our proof is unconditional for Ising lattice gauge theory, but relies on a regularity conjecture for the random-cluster model in slabs when $q>2.$ We also further develop the general theory of the $i$-plaquette random cluster model and its relationship with $(i-1)$-dimensional Potts lattice gauge |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_07534 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Sharp Deconfinement Transition for Potts Lattice Gauge Theory in Codimension Two Duncan, Paul Schweinhart, Benjamin Probability Mathematical Physics Algebraic Topology In 1983, Aizenman, Chayes, Chayes, Fröhlich, and Russo proved that $2$-dimensional Bernoulli plaquette percolation in $\mathbb{Z}^3$ exhibits a sharp phase transition for the event that a large rectangular loop is "bounded by a surface of plaquettes.'' We extend this result both to $(d-1)$-dimensional plaquette percolation in $\mathbb{Z}^d,$ and to a dependent model of plaquette percolation called the plaquette random-cluster model. As a consequence, we obtain a sharp phase transition for Wilson loop expectations in $(d-2)$-dimensional $q$-state Potts hyperlattice gauge theory on $\mathbb{Z}^d$ dual to that of the Potts model. Our proof is unconditional for Ising lattice gauge theory, but relies on a regularity conjecture for the random-cluster model in slabs when $q>2.$ We also further develop the general theory of the $i$-plaquette random cluster model and its relationship with $(i-1)$-dimensional Potts lattice gauge |
| title | A Sharp Deconfinement Transition for Potts Lattice Gauge Theory in Codimension Two |
| topic | Probability Mathematical Physics Algebraic Topology |
| url | https://arxiv.org/abs/2308.07534 |