Critical configurations of the hard-core model on square grid graphs
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866909596144107520 |
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| author | Baldassarri, Simone Jacquier, Vanessa Zocca, Alessandro |
| author_facet | Baldassarri, Simone Jacquier, Vanessa Zocca, Alessandro |
| contents | We consider the hard-core model on a finite square grid graph with stochastic Glauber dynamics parametrized by the inverse temperature $β$. We investigate how the transition between its two maximum-occupancy configurations takes place in the low-temperature regime $β\to\infty$ in the case of periodic boundary conditions. The hard-core constraints and the grid symmetry make the structure of the critical configurations, also known as essential saddles, for this transition very rich and complex. We provide a comprehensive geometrical characterization of the set of critical configurations that are asymptotically visited with probability one. In particular, we develop a novel isoperimetric inequality for hard-core configurations with a fixed number of particles and we show how not only their size but also their shape determines the characterization of the saddles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_05041 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Critical configurations of the hard-core model on square grid graphs Baldassarri, Simone Jacquier, Vanessa Zocca, Alessandro Probability Statistical Mechanics Mathematical Physics 82C20, 60J10, 60K35 We consider the hard-core model on a finite square grid graph with stochastic Glauber dynamics parametrized by the inverse temperature $β$. We investigate how the transition between its two maximum-occupancy configurations takes place in the low-temperature regime $β\to\infty$ in the case of periodic boundary conditions. The hard-core constraints and the grid symmetry make the structure of the critical configurations, also known as essential saddles, for this transition very rich and complex. We provide a comprehensive geometrical characterization of the set of critical configurations that are asymptotically visited with probability one. In particular, we develop a novel isoperimetric inequality for hard-core configurations with a fixed number of particles and we show how not only their size but also their shape determines the characterization of the saddles. |
| title | Critical configurations of the hard-core model on square grid graphs |
| topic | Probability Statistical Mechanics Mathematical Physics 82C20, 60J10, 60K35 |
| url | https://arxiv.org/abs/2308.05041 |