Replica symmetry up to the de Almeida-Thouless line in the Sherrington-Kirkpatrick model
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914470046990336 |
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| author | Lopatto, Patrick |
| author_facet | Lopatto, Patrick |
| contents | We show that in the Sherrington-Kirkpatrick model at inverse temperature $β$ with uniform external field $h>0$, replica symmetry holds in the regime $ β^2\mathrm{E}[ \mathrm{sech}^4(β\sqrt{q}Z+h)] \le 1$, where $Z$ is a standard Gaussian random variable. This confirms a prediction of de Almeida and Thouless (1978). The proof proceeds by a direct analysis of the Parisi measure using the characterization provided by Jagannath and Tobasco (2017). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_11921 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Replica symmetry up to the de Almeida-Thouless line in the Sherrington-Kirkpatrick model Lopatto, Patrick Probability Mathematical Physics We show that in the Sherrington-Kirkpatrick model at inverse temperature $β$ with uniform external field $h>0$, replica symmetry holds in the regime $ β^2\mathrm{E}[ \mathrm{sech}^4(β\sqrt{q}Z+h)] \le 1$, where $Z$ is a standard Gaussian random variable. This confirms a prediction of de Almeida and Thouless (1978). The proof proceeds by a direct analysis of the Parisi measure using the characterization provided by Jagannath and Tobasco (2017). |
| title | Replica symmetry up to the de Almeida-Thouless line in the Sherrington-Kirkpatrick model |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2604.11921 |