Recoverable systems and the maximal hard-core model on the triangular lattice
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918446753644544 |
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| author | Wang, Geyang Barg, Alexander Kashyap, Navin |
| author_facet | Wang, Geyang Barg, Alexander Kashyap, Navin |
| contents | In a previous paper (arXiv:2510.19746), we have studied the maximal hard-code model on the square lattice ${\mathbb Z}^2$ from the perspective of recoverable systems. Here we extend this study to the case of the triangular lattice ${\mathbb A}$. The following results are obtained:
(1) We derive bounds on the capacity of the associated recoverable system on ${\mathbb A}$;
(2) We show non-uniqueness of Gibbs measures in the high-activity regime;
(3) We characterize extremal periodic Gibbs measures for sufficiently low values of activity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_18310 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Recoverable systems and the maximal hard-core model on the triangular lattice Wang, Geyang Barg, Alexander Kashyap, Navin Combinatorics Discrete Mathematics Information Theory Probability In a previous paper (arXiv:2510.19746), we have studied the maximal hard-code model on the square lattice ${\mathbb Z}^2$ from the perspective of recoverable systems. Here we extend this study to the case of the triangular lattice ${\mathbb A}$. The following results are obtained: (1) We derive bounds on the capacity of the associated recoverable system on ${\mathbb A}$; (2) We show non-uniqueness of Gibbs measures in the high-activity regime; (3) We characterize extremal periodic Gibbs measures for sufficiently low values of activity. |
| title | Recoverable systems and the maximal hard-core model on the triangular lattice |
| topic | Combinatorics Discrete Mathematics Information Theory Probability |
| url | https://arxiv.org/abs/2602.18310 |