The monopole-dimer model on high-dimensional cylindrical, toroidal, Möbius and Klein grids
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913382488080384 |
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| author | Arora, Anita |
| author_facet | Arora, Anita |
| contents | The dimer (monomer-dimer) model deals with weighted enumeration of perfect matchings (matchings). The monopole-dimer model is a signed variant of the monomer-dimer model whose partition function is a determinant. In 1999, Lu and Wu evaluated the partition function of the dimer model on two-dimensional grids embedded on a Möbius strip and a Klein bottle. While the partition function of the dimer model has been known for the two-dimensional grids with different boundary conditions, we present a similar product formula for the partition function of the monopole-dimer model on higher dimensional cylindrical and toroidal grid graphs. We also evaluate the same for the three-dimensional Möbius and Klein grid graphs and show that the formula does not generalise for the higher dimensions. Further, we present a relation between the product formula for the three-dimensional cylindrical and Möbius grid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05750 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The monopole-dimer model on high-dimensional cylindrical, toroidal, Möbius and Klein grids Arora, Anita Combinatorics The dimer (monomer-dimer) model deals with weighted enumeration of perfect matchings (matchings). The monopole-dimer model is a signed variant of the monomer-dimer model whose partition function is a determinant. In 1999, Lu and Wu evaluated the partition function of the dimer model on two-dimensional grids embedded on a Möbius strip and a Klein bottle. While the partition function of the dimer model has been known for the two-dimensional grids with different boundary conditions, we present a similar product formula for the partition function of the monopole-dimer model on higher dimensional cylindrical and toroidal grid graphs. We also evaluate the same for the three-dimensional Möbius and Klein grid graphs and show that the formula does not generalise for the higher dimensions. Further, we present a relation between the product formula for the three-dimensional cylindrical and Möbius grid. |
| title | The monopole-dimer model on high-dimensional cylindrical, toroidal, Möbius and Klein grids |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2406.05750 |