{
  "abstract": "We study Glauber dynamics for the Ising model on random $d$-regular graphs with $n$ vertices at low temperature, in the regime $β\\geq C/d$ where $C,d$ are sufficiently large constants. In this regime, the full mixing time is exponential in $n$, because of the bottleneck between the two dominant phases: configurations with a majority of plus spins and configurations with a majority of minus spins. We show that, for sufficiently large $d$, if the dynamics is initialized with an excess of at least $ε_{C,d} n$ plus spins over minus spins, then it quasi-equilibrates in time $O(\\log n)$ to the Gibbs measure conditioned on positive magnetization. In addition, the required bias $ε_{C,d}$ can be chosen so that $ε_{C,d}\\to 0$ as $d,C\\to\\infty$. Previous bound of \\cite{GSS25+} in the Ising and large-$d$ setting required $β\\gtrsim (\\log d)/d$. A key difficulty is that, even from the all-plus initialization, one must control the propagation of negative information in spacetime in a low-temperature model with strong local correlations. We address this by developing a new bootstrap approach to proving subcriticality of disagreement clusters under the grand coupling.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27673",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhangsong Li"
    },
    {
      "name": "Allan Sly"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7hfxq43536n69.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27673",
  "fulltext_url": null,
  "id": "7hfxq43536n69",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27673",
  "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": "W7223083184",
  "pdf_url": "https://arxiv.org/pdf/2610.27673",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7hfxq43536n69.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2610.27673",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27673"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Improved rapid phase ordering for Ising dynamics on random regular graphs",
  "title_text": "Improved rapid phase ordering for Ising dynamics on random regular graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/7hfxq43536n69",
  "venue": "arXiv",
  "versions": []
}