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  "slug": "ferromagnetic-full-threshold-glauber",
  "title": "Near-linear Glauber mixing below the full ferromagnetic field threshold",
  "shortTitle": "A controlled core, a faster mixing bound",
  "url": "https://evidencepress.org/releases/ferromagnetic-full-threshold-glauber/",
  "oneLine": "A candidate near-linear single-site mixing bound covers the full strict field range of a heterogeneous ferromagnetic class, with unrestricted degrees and arbitrary starts.",
  "abstract": "An unrefereed written-proof candidate establishes O_{β,γ,λ}(n log²(2n) log(1/ε)) worst-start single-site heatbath mixing throughout the strict Feng–Guo–Yang heterogeneous ferromagnetic envelope λ < λc(β,γ). An integrable scalar covariance rate and deterministic degree/bias trimming allow an existing Miao–Yin entropy criterion to be applied to a residual law, followed by finite-horizon comparison with the original dynamics. A direct imported gap comparison also gives linear relaxation for the untrimmed chain. The threshold endpoint, an O(n log n) mixing bound, a uniform ordinary log–Sobolev constant for the original law and measured runtime gains are not established.",
  "datePublished": "2026-10-14",
  "dateModified": "2026-10-14",
  "version": "2.0.0-candidate",
  "doi": "10.5281/zenodo.23359097",
  "doiUrl": "https://doi.org/10.5281/zenodo.23359097",
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  "authors": [
    "Anonymous"
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  "status": "unrefereed-candidate",
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      "note": "Supplied finite audit and fresh public exact diagnostics passed normal and optimized execution; seven semantic negative controls rejected. Universal and imported analytic statements remain written proofs.",
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      "dimension": "independentRerun",
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      "dimension": "independentReimplementation",
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      "label": "Formal verification",
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      "state": "not-assessed",
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      "question": "Are data and computational environment pinned well enough to rebuild?",
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      "evidenceUrl": "https://github.com/ipitchford/ferromagnetic-full-threshold-glauber/blob/v2.0.0-candidate/ENVIRONMENT.txt",
      "note": "Python standard-library diagnostics and version information supplied. No hermetic reconstruction or unaffiliated reproduction established."
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    "reviewStatus": "Coordinated internal analytic checking and supplied referee-style material; no external human peer review established."
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  "attributionBoundary": null,
  "problem": {
    "name": "Near-linear worst-start mixing throughout the strict heterogeneous ferromagnetic field range",
    "url": "https://arxiv.org/abs/2604.00963v2"
  },
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  "metadataProvenance": "Revised manuscript, archive-bound replay and scoped internal proof checks, 14 October 2026; public availability is assessed separately.",
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  "keywords": [
    "ferromagnetic spin systems",
    "Glauber dynamics",
    "worst-start mixing",
    "spectral independence",
    "deterministic pinning",
    "log-Sobolev inequality",
    "spectral gap"
  ],
  "keyResults": [
    "A candidate O(n log²(2n) log(1/ε)) single-site update bound throughout the stated strict field envelope, uniform in degrees and admissible heterogeneous parameters.",
    "A pinned scalar covariance rate 1 + As makes the required stability integral finite.",
    "Deterministic high-degree/high-bias trimming and a finite-horizon coupling remove original marginal and startup restrictions from the mixing argument.",
    "An imported comparison gives a linear relaxation bound for the untrimmed chain; explicit examples separate this from a uniform ordinary entropy inequality."
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  "evidencePackage": "Written analytic proof; a public original checker verifies 22,323 exact rational equalities across five models and 459 pinning/tilt laws, with seven semantic negative controls in normal and optimized execution. A distinct supplied private floating-point audit covers 75 models, 855 pinned covariance cases and 7,440 state/schedule pairs; its code is not redistributed. These finite checks do not establish the universal theorem.",
  "openProblems": [],
  "mathObjects": [],
  "relatedWorks": [
    {
      "citation": "Feng, Guo and Yang, Rapid mixing in positively weighted restricted Boltzmann machines, arXiv:2604.00963v2. Definition 4, Theorems 5–6 and 24, Proposition 14 and the computation-tree comparison.",
      "url": "https://arxiv.org/abs/2604.00963v2",
      "doi": "10.48550/arXiv.2604.00963"
    },
    {
      "citation": "Miao and Yin, Sampling Matchings in Near-linear Time, arXiv:2609.21936v1. Definition 1.1, Theorem 1.4, Proposition 2.1 and Section 2.1 supply the imported scalar-field entropy and gap criteria.",
      "url": "https://arxiv.org/abs/2609.21936v1",
      "doi": "10.48550/arXiv.2609.21936"
    },
    {
      "citation": "Chen, Feng, Yin and Zhang, Optimal mixing for two-state anti-ferromagnetic spin systems, arXiv:2203.07771v1. Definition 1.9 and Theorem 1.11 provide the alternative relative-marginal-stability comparison.",
      "url": "https://arxiv.org/abs/2203.07771v1",
      "doi": "10.48550/arXiv.2203.07771"
    }
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