Free energy fluctuations in SK and related spin glass models: A literature survey
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908636344745984 |
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| author | Collins-Woodfin, Elizabeth Le, Han Gia |
| author_facet | Collins-Woodfin, Elizabeth Le, Han Gia |
| contents | Over the past 50 years, spin glass models have generated a broad range of literature in mathematics, physics, and computer science. There has been much progress in characterizing and proving the limiting free energy of various models, stemming from the original formulas of Parisi. Comparatively less is known about the more detailed topic of free energy fluctuations. This paper concerns a family of models in which there has been considerable progress on fluctuations, namely the Sherrington-Kirkpatrick (SK) and spherical Sherrington-Kirkpatrick (SSK) models, along with their multi-species analogs. We present a survey of the literature on free energy fluctuations in these 2-spin models, discussing results from different temperature regimes, with and without an external field, including results on phase transitions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_26960 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Free energy fluctuations in SK and related spin glass models: A literature survey Collins-Woodfin, Elizabeth Le, Han Gia Probability Mathematical Physics 60K35, 82B44, 82D30 Over the past 50 years, spin glass models have generated a broad range of literature in mathematics, physics, and computer science. There has been much progress in characterizing and proving the limiting free energy of various models, stemming from the original formulas of Parisi. Comparatively less is known about the more detailed topic of free energy fluctuations. This paper concerns a family of models in which there has been considerable progress on fluctuations, namely the Sherrington-Kirkpatrick (SK) and spherical Sherrington-Kirkpatrick (SSK) models, along with their multi-species analogs. We present a survey of the literature on free energy fluctuations in these 2-spin models, discussing results from different temperature regimes, with and without an external field, including results on phase transitions. |
| title | Free energy fluctuations in SK and related spin glass models: A literature survey |
| topic | Probability Mathematical Physics 60K35, 82B44, 82D30 |
| url | https://arxiv.org/abs/2510.26960 |