On zeros and algorithms for disordered systems: mean-field spin glasses
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918188625690624 |
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| author | Bencs, Ferenc Huang, Brice Lee, Daniel Z. Liu, Kuikui Regts, Guus |
| author_facet | Bencs, Ferenc Huang, Brice Lee, Daniel Z. Liu, Kuikui Regts, Guus |
| contents | Spin glasses are fundamental probability distributions at the core of statistical physics, the theory of average-case computational complexity, and modern high-dimensional statistical inference. In the mean-field setting, we design deterministic quasipolynomial-time algorithms for estimating the partition function to arbitrarily high accuracy for all inverse temperatures in the second moment regime. In particular, for the Sherrington--Kirkpatrick model, our algorithms succeed for the entire replica-symmetric phase. To achieve this, we study the locations of the zeros of the partition function. Notably, our methods are conceptually simple, and apply equally well to the spherical case and the case of Ising spins. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15616 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On zeros and algorithms for disordered systems: mean-field spin glasses Bencs, Ferenc Huang, Brice Lee, Daniel Z. Liu, Kuikui Regts, Guus Data Structures and Algorithms Disordered Systems and Neural Networks Discrete Mathematics Mathematical Physics Probability Spin glasses are fundamental probability distributions at the core of statistical physics, the theory of average-case computational complexity, and modern high-dimensional statistical inference. In the mean-field setting, we design deterministic quasipolynomial-time algorithms for estimating the partition function to arbitrarily high accuracy for all inverse temperatures in the second moment regime. In particular, for the Sherrington--Kirkpatrick model, our algorithms succeed for the entire replica-symmetric phase. To achieve this, we study the locations of the zeros of the partition function. Notably, our methods are conceptually simple, and apply equally well to the spherical case and the case of Ising spins. |
| title | On zeros and algorithms for disordered systems: mean-field spin glasses |
| topic | Data Structures and Algorithms Disordered Systems and Neural Networks Discrete Mathematics Mathematical Physics Probability |
| url | https://arxiv.org/abs/2507.15616 |