{
  "abstract": "We prove blue percolation in the Chayes-Machta-Redner representation of the zero-field Edwards-Anderson spin glass in finite dimensions. For fixed symmetric iid couplings with $0<m=\\mathbb{E}|J|<\\infty$, the first blue-percolation inverse temperature $β_{\\mathrm{b}}(d)$ satisfies $2dm\\,β_{\\mathrm{b}}(d)\\to1$ as $d\\to\\infty$, in periodic joint limits. For symmetric $\\pm1$ couplings, both overlap signs percolate at explicit temperatures in every dimension from 7 to 12. That proof reveals the overlap field, shows that it dominates a weakly coupled Ising field, and bounds a weighted second moment of open paths; in dimensions 7 to 9 the paths make short lateral excursions, and an interaction-matrix criterion controls the second moment. These proofs are computer-assisted: finitely many inequalities between rigorously bounded quantities are decided in exact rational arithmetic. For exponential-moment disorder, we also establish a percolating regime with exactly equal infinite-blue-sector densities and finite spin-glass susceptibility. In these periodic limits, persistent density imbalance would imply distinct spin-flip-related Gibbs states and ordinary spin-glass order: positive spatial-overlap variance, infinite spin-glass susceptibility and a cusp of the replica-coupling pressure, without requiring finite-blue cancellation. Proving imbalance remains open.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22301",
  "author_total": 1,
  "authors": [
    {
      "name": "Yan Ru Pei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ekjnk8nacxtz9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22301",
  "fulltext_url": null,
  "id": "ekjnk8nacxtz9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22301",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "3104|Theoretical and Computational Physics"
    ]
  ],
  "openalex": "W7214045687",
  "pdf_url": "https://arxiv.org/pdf/2609.22301",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ekjnk8nacxtz9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:48Z",
      "native_id": "2609.22301",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22301"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Towards the spin-glass transition in finite dimensions via blue percolation",
  "title_text": "Towards the spin-glass transition in finite dimensions via blue percolation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/ekjnk8nacxtz9",
  "venue": "arXiv",
  "versions": []
}