On the de Almeida--Thouless Transition Surface in the Multi-Species SK Model with Centered Gaussian External Field
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908670538809344 |
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| author | Kim, Heejune |
| author_facet | Kim, Heejune |
| contents | We study the phase transition of the Parisi formula for the free energy in the multi-species Sherrington--Kirkpatrick model with a centered Gaussian external field and a positive-semidefinite variance profile matrix. We show that in terms of the strength of the external field and the variance profile, the de Almeida--Thouless surface delineates the boundary between replica symmetric solutions and replica symmetry breaking solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18066 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the de Almeida--Thouless Transition Surface in the Multi-Species SK Model with Centered Gaussian External Field Kim, Heejune Probability Mathematical Physics We study the phase transition of the Parisi formula for the free energy in the multi-species Sherrington--Kirkpatrick model with a centered Gaussian external field and a positive-semidefinite variance profile matrix. We show that in terms of the strength of the external field and the variance profile, the de Almeida--Thouless surface delineates the boundary between replica symmetric solutions and replica symmetry breaking solutions. |
| title | On the de Almeida--Thouless Transition Surface in the Multi-Species SK Model with Centered Gaussian External Field |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2509.18066 |