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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2511.20163 |
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| _version_ | 1866917405491462144 |
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| author | Delfino, Gesualdo |
| author_facet | Delfino, Gesualdo |
| contents | We recently showed that the two-dimensional Ising spin glass allows for a line of renormalization group fixed points which explains properties observed in numerical studies. We observe that this exact result corresponds to enhancement to a one-generator continuous internal symmetry. This finally explains why no finite temperature transition to a spin glass phase is observed in two dimensions. In more than two dimensions, instead, the continuous symmetry can be broken spontaneously and yields a spin glass order parameter which, for fixed temperature and disorder strength, takes continuous values in an interval. Such a feature is shared by the order parameter of the known mean field solution of the model with infinite-range interactions, which corresponds to infinitely many dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20163 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the nature of the spin glass transition Delfino, Gesualdo Statistical Mechanics Disordered Systems and Neural Networks High Energy Physics - Theory We recently showed that the two-dimensional Ising spin glass allows for a line of renormalization group fixed points which explains properties observed in numerical studies. We observe that this exact result corresponds to enhancement to a one-generator continuous internal symmetry. This finally explains why no finite temperature transition to a spin glass phase is observed in two dimensions. In more than two dimensions, instead, the continuous symmetry can be broken spontaneously and yields a spin glass order parameter which, for fixed temperature and disorder strength, takes continuous values in an interval. Such a feature is shared by the order parameter of the known mean field solution of the model with infinite-range interactions, which corresponds to infinitely many dimensions. |
| title | On the nature of the spin glass transition |
| topic | Statistical Mechanics Disordered Systems and Neural Networks High Energy Physics - Theory |
| url | https://arxiv.org/abs/2511.20163 |