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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2411.17497 |
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| _version_ | 1866917849083150336 |
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| author | Shvalyuk, Daria Nazarov, Anton |
| author_facet | Shvalyuk, Daria Nazarov, Anton |
| contents | In this paper, we consider the formation of droplets in the dimer model on a triangular lattice. The droplets in the dimer model are superposition polygons formed as two overlapping configurations of dimers: constant and movable. We demonstrate that specific local energies of dimers and low temperatures lead to the emergence of a macroscopic droplet. The motivation for this study was the phenomenon of the formation of equilibrium droplets under certain conditions in the Ising model within the framework of the Dobrushin-Kotecký-Shlosman theory. Due to the deep connections between the Ising model and the dimer model, similar behaviour was expected. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17497 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Observation of droplets in dimer model on a triangular lattice Shvalyuk, Daria Nazarov, Anton Statistical Mechanics Mathematical Physics Computational Physics 82B20, 05C70, 82M31 J.2; G.3 In this paper, we consider the formation of droplets in the dimer model on a triangular lattice. The droplets in the dimer model are superposition polygons formed as two overlapping configurations of dimers: constant and movable. We demonstrate that specific local energies of dimers and low temperatures lead to the emergence of a macroscopic droplet. The motivation for this study was the phenomenon of the formation of equilibrium droplets under certain conditions in the Ising model within the framework of the Dobrushin-Kotecký-Shlosman theory. Due to the deep connections between the Ising model and the dimer model, similar behaviour was expected. |
| title | Observation of droplets in dimer model on a triangular lattice |
| topic | Statistical Mechanics Mathematical Physics Computational Physics 82B20, 05C70, 82M31 J.2; G.3 |
| url | https://arxiv.org/abs/2411.17497 |