Uniqueness and CLT for the Ground State of the Disordered Monomer-Dimer Model on $\mathbb{Z}^{d}$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914840177541120 |
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| author | Krishnan, Kesav Ray, Gourab |
| author_facet | Krishnan, Kesav Ray, Gourab |
| contents | We prove that the disordered monomer-dimer model does not admit infinite volume incongruent ground states in $\mathbb{Z}^d$ which can be obtained as a limit of finite volume ground states. Furthermore, we also prove that these ground states are stable under perturbation of the weights in a precise sense.
As an application, we obtain a CLT for the ground state weight for a growing sequence of tori. Our motivation stems from a similar and long standing open question for the short range Edwards-Anderson spin glass model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13089 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniqueness and CLT for the Ground State of the Disordered Monomer-Dimer Model on $\mathbb{Z}^{d}$ Krishnan, Kesav Ray, Gourab Mathematical Physics Probability Primary: 60F05, Secondary: 82B44, Tertiary: 82B20 We prove that the disordered monomer-dimer model does not admit infinite volume incongruent ground states in $\mathbb{Z}^d$ which can be obtained as a limit of finite volume ground states. Furthermore, we also prove that these ground states are stable under perturbation of the weights in a precise sense. As an application, we obtain a CLT for the ground state weight for a growing sequence of tori. Our motivation stems from a similar and long standing open question for the short range Edwards-Anderson spin glass model. |
| title | Uniqueness and CLT for the Ground State of the Disordered Monomer-Dimer Model on $\mathbb{Z}^{d}$ |
| topic | Mathematical Physics Probability Primary: 60F05, Secondary: 82B44, Tertiary: 82B20 |
| url | https://arxiv.org/abs/2406.13089 |