Free energy equivalence between mean-field models and nonsparsely diluted mean-field models
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908197045927936 |
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| author | Okuyama, Manaka Ohzeki, Masayuki |
| author_facet | Okuyama, Manaka Ohzeki, Masayuki |
| contents | We studied nonsparsely diluted mean-field models that differ from sparsely diluted mean-field models, such as the Viana--Bray model. When the existence probability of each edge follows a Bernoulli distribution, we rigorously prove that the free energy of nonsparsely diluted mean-field models with appropriate parameterization coincides exactly with that of the corresponding mean-field models in ferromagnetic and spin-glass models composed of any discrete spin $S$ in the thermodynamic limit. Our results is a broad generalization of the result of a previous study [Bovier and Gayrard, J. Stat. Phys. 72, 643 (1993)], where the densely diluted mean-field ferromagnetic Ising model (diluted Curie--Weiss model) with appropriate parameterization was analyzed rigorously, and it was proven that its free energy was exactly equivalent to that of the corresponding mean-field model (Curie--Weiss model). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13245 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Free energy equivalence between mean-field models and nonsparsely diluted mean-field models Okuyama, Manaka Ohzeki, Masayuki Disordered Systems and Neural Networks Statistical Mechanics Mathematical Physics Probability We studied nonsparsely diluted mean-field models that differ from sparsely diluted mean-field models, such as the Viana--Bray model. When the existence probability of each edge follows a Bernoulli distribution, we rigorously prove that the free energy of nonsparsely diluted mean-field models with appropriate parameterization coincides exactly with that of the corresponding mean-field models in ferromagnetic and spin-glass models composed of any discrete spin $S$ in the thermodynamic limit. Our results is a broad generalization of the result of a previous study [Bovier and Gayrard, J. Stat. Phys. 72, 643 (1993)], where the densely diluted mean-field ferromagnetic Ising model (diluted Curie--Weiss model) with appropriate parameterization was analyzed rigorously, and it was proven that its free energy was exactly equivalent to that of the corresponding mean-field model (Curie--Weiss model). |
| title | Free energy equivalence between mean-field models and nonsparsely diluted mean-field models |
| topic | Disordered Systems and Neural Networks Statistical Mechanics Mathematical Physics Probability |
| url | https://arxiv.org/abs/2406.13245 |