A Multi-Body Dobrushin-Sokal Criterion -- Part I
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911107482910720 |
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| author | Neumann, Jan Philipp |
| author_facet | Neumann, Jan Philipp |
| contents | We derive a sufficient condition for zero-freeness of partition functions applicable to lattice gases with possibly complex-valued multi-body interactions. This includes the case of hard-core interactions and, in particular, generalises recent results by Galvin et al.\ (2024) and Bencs-Buys (2025) on zero-free polydiscs of hypergraph independence polynomials. We provide two proofs: the first generalises the inductive approach of Bencs and Buys; the second employs the Kirkwood-Salsburg hierarchy. Notably, the central argument of the second proof uses of a certain partition scheme for coverings and, as a by-product, we obtain a direct improvement of Gallavotti and Miracle-Solé's (1968) bounds for the Kirkwood-Salsburg operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12078 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Multi-Body Dobrushin-Sokal Criterion -- Part I Neumann, Jan Philipp Mathematical Physics Combinatorics 82B20 (Primary) 05C31, 05C65, 05C69 (Secondary) We derive a sufficient condition for zero-freeness of partition functions applicable to lattice gases with possibly complex-valued multi-body interactions. This includes the case of hard-core interactions and, in particular, generalises recent results by Galvin et al.\ (2024) and Bencs-Buys (2025) on zero-free polydiscs of hypergraph independence polynomials. We provide two proofs: the first generalises the inductive approach of Bencs and Buys; the second employs the Kirkwood-Salsburg hierarchy. Notably, the central argument of the second proof uses of a certain partition scheme for coverings and, as a by-product, we obtain a direct improvement of Gallavotti and Miracle-Solé's (1968) bounds for the Kirkwood-Salsburg operator. |
| title | A Multi-Body Dobrushin-Sokal Criterion -- Part I |
| topic | Mathematical Physics Combinatorics 82B20 (Primary) 05C31, 05C65, 05C69 (Secondary) |
| url | https://arxiv.org/abs/2508.12078 |