Non-local Potts model on random lattice and chromatic number of a plane
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866914426023575552 |
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| author | Shevchenko, V. Tanashkin, A. |
| author_facet | Shevchenko, V. Tanashkin, A. |
| contents | Statistical models are widely used for the investigation of complex system's behavior. Most of the models considered in the literature are formulated on regular lattices with nearest-neighbor interactions. The models with non-local interaction kernels have been less studied. In this article, we investigate an example of such a model - the non-local q-color Potts model on a random d=2 lattice. Only the same color spins at a unit distance (within some small margin $δ$) interact. We study the vacuum states of this model and present the results of numerical simulations and discuss qualitative features of the corresponding patterns. Conjectured relation with the chromatic number of a plane problem is discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_08508 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Non-local Potts model on random lattice and chromatic number of a plane Shevchenko, V. Tanashkin, A. Computational Physics Disordered Systems and Neural Networks Combinatorics Statistical models are widely used for the investigation of complex system's behavior. Most of the models considered in the literature are formulated on regular lattices with nearest-neighbor interactions. The models with non-local interaction kernels have been less studied. In this article, we investigate an example of such a model - the non-local q-color Potts model on a random d=2 lattice. Only the same color spins at a unit distance (within some small margin $δ$) interact. We study the vacuum states of this model and present the results of numerical simulations and discuss qualitative features of the corresponding patterns. Conjectured relation with the chromatic number of a plane problem is discussed. |
| title | Non-local Potts model on random lattice and chromatic number of a plane |
| topic | Computational Physics Disordered Systems and Neural Networks Combinatorics |
| url | https://arxiv.org/abs/2107.08508 |