Liquid-Gas phase transition for Gibbs point process with Quermass interaction
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866915633298407424 |
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| author | Dereudre, David Renaud-Chan, Christopher |
| author_facet | Dereudre, David Renaud-Chan, Christopher |
| contents | We prove the existence of a liquid-gas phase transition for continuous Gibbs point process in $\mathbb{R}^d$ with Quermass interaction. The Hamiltonian we consider is a linear combination of the volume $\mathcal{V}$, the surface measure $\mathcal{S}$ and the Euler-Poincaré characteristic $χ$ of a halo of particles (i.e. an union of balls centred at the positions of particles). We show the non-uniqueness of infinite volume Gibbs measures for special values of activity and temperature, provided that the temperature is low enough. Moreover we show the non-differentiability of the pressure at these critical points. Our main tool is an adaptation of the Pirogov-Sinaï-Zahradnik theory for continuous systems with interaction exhibiting a saturation property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_08338 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Liquid-Gas phase transition for Gibbs point process with Quermass interaction Dereudre, David Renaud-Chan, Christopher Probability Mathematical Physics 60D05 (Primary), 82B21, 82B26 We prove the existence of a liquid-gas phase transition for continuous Gibbs point process in $\mathbb{R}^d$ with Quermass interaction. The Hamiltonian we consider is a linear combination of the volume $\mathcal{V}$, the surface measure $\mathcal{S}$ and the Euler-Poincaré characteristic $χ$ of a halo of particles (i.e. an union of balls centred at the positions of particles). We show the non-uniqueness of infinite volume Gibbs measures for special values of activity and temperature, provided that the temperature is low enough. Moreover we show the non-differentiability of the pressure at these critical points. Our main tool is an adaptation of the Pirogov-Sinaï-Zahradnik theory for continuous systems with interaction exhibiting a saturation property. |
| title | Liquid-Gas phase transition for Gibbs point process with Quermass interaction |
| topic | Probability Mathematical Physics 60D05 (Primary), 82B21, 82B26 |
| url | https://arxiv.org/abs/2309.08338 |