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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.08043 |
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| _version_ | 1866916296239611904 |
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| author | Duncan, Paul Schweinhart, Benjamin |
| author_facet | Duncan, Paul Schweinhart, Benjamin |
| contents | We show that the $i$-dimensional plaqutte random-cluster model with coefficients in $\mathbb{Z}_q$ is dual to a $(d-i)$-dimensional plaquette random cluster model. In addition, we explore boundary conditions, infinite volume limits, and uniqueness for these models. For previously known results, we provide new proofs that rely more on the tools of algebraic topology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08043 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some Properties of the Plaquette Random-Cluster Model Duncan, Paul Schweinhart, Benjamin Probability Mathematical Physics Algebraic Topology We show that the $i$-dimensional plaqutte random-cluster model with coefficients in $\mathbb{Z}_q$ is dual to a $(d-i)$-dimensional plaquette random cluster model. In addition, we explore boundary conditions, infinite volume limits, and uniqueness for these models. For previously known results, we provide new proofs that rely more on the tools of algebraic topology. |
| title | Some Properties of the Plaquette Random-Cluster Model |
| topic | Probability Mathematical Physics Algebraic Topology |
| url | https://arxiv.org/abs/2406.08043 |