{
  "abstract": "We study Glauber dynamics for Ising measures conditioned to have a sufficiently large majority of $+1$ spins. Under a sparse spectral width condition on the interaction matrix, we derive a Poincaré inequality for the conditioned measures from a magnetization drift condition, and a modified logarithmic Sobolev inequality from a stronger, entropy weighted condition. As applications, we obtain approximate posterior sampling in total variation distance for $\\mathbb{Z}_2$ synchronization at high enough signal-to-noise ratio using $O(n\\log n)$ Glauber updates from a spectral initialization. For ferromagnetic Ising models on random $d$-regular graphs, we prove rapid phase ordering down to inverse temperatures of order $1/d$, extending the temperature range of Gheissari, Sly, and Sohn (2025). Finally, we extend these inequalities to unconditioned Ising measures under an inward drift condition outside the conditioned region. This yields $O(n\\log n)$ mixing of Glauber dynamics for the Sherrington-Kirkpatrick model at every fixed inverse temperature when the external field is sufficiently large.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23777",
  "author_total": 2,
  "authors": [
    {
      "name": "Vasyl Paliy"
    },
    {
      "name": "Youngtak Sohn"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/80wf0m0jzspr4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23777",
  "fulltext_url": null,
  "id": "80wf0m0jzspr4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23777",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7222955976",
  "pdf_url": "https://arxiv.org/pdf/2610.23777",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/80wf0m0jzspr4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:32Z",
      "native_id": "2610.23777",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23777"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Rapid mixing within a phase for Ising models",
  "title_text": "Rapid mixing within a phase for Ising models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/80wf0m0jzspr4",
  "venue": "arXiv",
  "versions": []
}