Optimal Mixing of Glauber Dynamics for the Sherrington-Kirkpatrick Model at $β< 1/2$

[2608.22159] Optimal Mixing of Glauber Dynamics for the Sherrington-Kirkpatrick Model at $β< 1/2$ Skip to main content Search Submit Donate Log in Mathematics > Probability arXiv:2608.22159 (math) [Submitted on 23 Aug 2026 ( v1 ), last revised 28 Aug 2026 (this version, v2)] Title: Optimal Mixing of Glauber Dynamics for the Sherrington-Kirkpatrick Model at $β< 1/2$ Authors: Sihan Wang View PDF HTML (experimental) Abstract: We prove that for every fixed inverse temperature $\beta < 1 / 2$, with high probability over the disorder, the single-site Glauber dynamics for the $n$-spin Sherrington-Kirkpatrick model mixes from every initial configuration to within total variation distance $\varepsilon$ in $O_{\beta}\left(n \log\left(n / \varepsilon\right)\right)$ steps. The bound holds uniformly over all external fields and is optimal up to constants depending only on $\beta$. The main ingredient is a deterministic criterion for optimal-order Poincaré inequalities in general Ising models, established via the integrated Bakry-Émery criterion together with a new two-spin estimate. A standard application of the localization-scheme framework of Chen and Eldan then upgrades the Poincaré inequality to a modified log-Sobolev inequality, yielding the optimal mixing-time bound. The main ideas underlying the proof of the Poincaré inequality were generated by GPT-5.6 Sol Ultra. Comments: Revised version; added related references and improved exposition Subjects: Probability (math.PR) ; Data Structures and Algorithms (cs.DS); Mathematical Physics (math-ph) Cite as: arXiv:2608.22159 [math.PR] (or arXiv:2608.22159v2 [math.PR] for this version) https://doi.org/10.48550/arXiv.2608.22159 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Sihan Wang [ view email ] [v1] Sun, 23 Aug 2026 01:18:21 UTC (19 KB) [v2] Fri, 28 Aug 2026 05:23:09 UTC (20 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.PR < prev | next > new | recent | 2026-08 Change to browse by: cs cs.DS math math-ph math.MP References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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