Exponentially Slow Mixing of the Low Temperature SK Model
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918239542444032 |
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| author | Sellke, Mark |
| author_facet | Sellke, Mark |
| contents | We give a short proof that low-temperature dynamics for the Sherrington-Kirkpatrick model have mixing time exponential in the system size, based on the recently proved existence of gapped spin configurations by (Minzer-Sah-Sawhney 2023, Dandi-Gamarnik-Zdeborová 2023). This result is in contrast with a well established physics prediction which posits a stretched exponential mixing time of order $e^{N^{1/3 \pm o(1)}}$. Our proof clarifies that this prediction cannot apply to mixing from worst case initial conditions, but should presumably be understood to concern dynamics from a suitably random initialization. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_22621 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exponentially Slow Mixing of the Low Temperature SK Model Sellke, Mark Probability Disordered Systems and Neural Networks Mathematical Physics We give a short proof that low-temperature dynamics for the Sherrington-Kirkpatrick model have mixing time exponential in the system size, based on the recently proved existence of gapped spin configurations by (Minzer-Sah-Sawhney 2023, Dandi-Gamarnik-Zdeborová 2023). This result is in contrast with a well established physics prediction which posits a stretched exponential mixing time of order $e^{N^{1/3 \pm o(1)}}$. Our proof clarifies that this prediction cannot apply to mixing from worst case initial conditions, but should presumably be understood to concern dynamics from a suitably random initialization. |
| title | Exponentially Slow Mixing of the Low Temperature SK Model |
| topic | Probability Disordered Systems and Neural Networks Mathematical Physics |
| url | https://arxiv.org/abs/2511.22621 |