A Cellular Representation of the Potts Lattice Higgs Model
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918356822523904 |
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| author | Eldridge, Summer Forsström, Malin P. Schweinhart, Benjamin |
| author_facet | Eldridge, Summer Forsström, Malin P. Schweinhart, Benjamin |
| contents | The $i$-dimensional Potts lattice Higgs model is a random assignment of spins in $\mathbb{Z}_q$ to the $i$-dimensional cells of a cell complex induced by a Hamiltonian with a Potts interaction on the $(i+1)$-cells and an additional term playing the role of an external field. We develop a representation of this model as a pair of dependent plaquette percolations, and prove that Wilson line expectations can be expressed in terms of the probability of a topological event. As an application, we prove the existence of a phase transition for the Marcu--Fredenhagen ratio in the Potts lattice Higgs model on $\mathbb{Z}^d$ when $i=1.$ |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_22199 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Cellular Representation of the Potts Lattice Higgs Model Eldridge, Summer Forsström, Malin P. Schweinhart, Benjamin Probability Mathematical Physics The $i$-dimensional Potts lattice Higgs model is a random assignment of spins in $\mathbb{Z}_q$ to the $i$-dimensional cells of a cell complex induced by a Hamiltonian with a Potts interaction on the $(i+1)$-cells and an additional term playing the role of an external field. We develop a representation of this model as a pair of dependent plaquette percolations, and prove that Wilson line expectations can be expressed in terms of the probability of a topological event. As an application, we prove the existence of a phase transition for the Marcu--Fredenhagen ratio in the Potts lattice Higgs model on $\mathbb{Z}^d$ when $i=1.$ |
| title | A Cellular Representation of the Potts Lattice Higgs Model |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2602.22199 |