First-order phase transition for Gibbs point processes with saturated interactions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911441220534272 |
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| author | Dereudre, David Renaud-Chan, Christopher |
| author_facet | Dereudre, David Renaud-Chan, Christopher |
| contents | We study first-order phase transitions in continuum Gibbs point processes with saturated interactions. These interactions form a broad class of Hamiltonians in which the local energy in regions of high particle density depends only on the number of points. Building on ideas of Pirogov-Sinai-Zahradnik theory and its adaptations to the continuum, we develop a general method for establishing the existence of two distinct infinite-volume Gibbs measures with different intensities in this setting, demonstrating a first-order phase transition. Our approach extends previous results obtained for the Quermass model and applies in particular to a new class of diluted pairwise interactions introduced in this work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11078 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | First-order phase transition for Gibbs point processes with saturated interactions Dereudre, David Renaud-Chan, Christopher Probability Mathematical Physics 60G55 (Primary), 82B21, 82B26 (Secondary) We study first-order phase transitions in continuum Gibbs point processes with saturated interactions. These interactions form a broad class of Hamiltonians in which the local energy in regions of high particle density depends only on the number of points. Building on ideas of Pirogov-Sinai-Zahradnik theory and its adaptations to the continuum, we develop a general method for establishing the existence of two distinct infinite-volume Gibbs measures with different intensities in this setting, demonstrating a first-order phase transition. Our approach extends previous results obtained for the Quermass model and applies in particular to a new class of diluted pairwise interactions introduced in this work. |
| title | First-order phase transition for Gibbs point processes with saturated interactions |
| topic | Probability Mathematical Physics 60G55 (Primary), 82B21, 82B26 (Secondary) |
| url | https://arxiv.org/abs/2602.11078 |