Replica bound for Ising spin glass models in one dimension
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909429339783168 |
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| author | Okuyama, Manaka Ohzeki, Masayuki |
| author_facet | Okuyama, Manaka Ohzeki, Masayuki |
| contents | The interpolation method is a powerful tool for rigorous analysis of mean-field spin glass models, both with and without dilution. In this study, we show that the interpolation method can be applied to Ising spin glass models in one dimension, such as a one-dimensional chain and a two-leg ladder. In one dimension, the replica symmetric (RS) cavity method is naturally expected to be rigorous for Ising spin glass models. Using the interpolation method, we rigorously prove that the RS cavity method provides lower bounds on the quenched free energies of Ising spin glass models in one dimension at any finite temperature in the thermodynamic limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_14857 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Replica bound for Ising spin glass models in one dimension Okuyama, Manaka Ohzeki, Masayuki Disordered Systems and Neural Networks Statistical Mechanics Mathematical Physics The interpolation method is a powerful tool for rigorous analysis of mean-field spin glass models, both with and without dilution. In this study, we show that the interpolation method can be applied to Ising spin glass models in one dimension, such as a one-dimensional chain and a two-leg ladder. In one dimension, the replica symmetric (RS) cavity method is naturally expected to be rigorous for Ising spin glass models. Using the interpolation method, we rigorously prove that the RS cavity method provides lower bounds on the quenched free energies of Ising spin glass models in one dimension at any finite temperature in the thermodynamic limit. |
| title | Replica bound for Ising spin glass models in one dimension |
| topic | Disordered Systems and Neural Networks Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2406.14857 |