{
  "abstract": "We prove a lower comparison for disorder-averaged ferromagnetic XY correlations: independent nonnegative random couplings $K_e$ can be replaced by $-\\frac12\\log\\mathbb{E}e^{-2K_e}$. Ginibre's inequality makes each normalized correlation convex in $1-e^{-2K_e}$, so conditional Jensen and thinning compare Bernoulli bond densities; two star-wise Jensen passes handle site dilution on bipartite graphs. Together with the phase-existence theorem of Dario and Garban, these comparisons give local Lipschitz regularity of both the averaged algebraic-phase and susceptibility-divergence thresholds throughout the supercritical density intervals on $\\mathbb{Z}^2$. The clean finite-domain criterion of van Engelenburg and Lis also yields explicit finite-size susceptibility lower bounds in a weak-dilution region. For bounded centered bond noise, the possible suppression of the algebraic-phase temperature is at most quadratic in the noise amplitude. Finally, at finite positive thresholds we prove total-variation continuity for bounded iid coupling laws whose essential supremum equals the common support cap, with local Lipschitz control when the reference law has an atom at that cap.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14201",
  "author_total": 1,
  "authors": [
    {
      "name": "Yan Ru Pei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5j5s8t0rf9sw0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14201",
  "fulltext_url": null,
  "id": "5j5s8t0rf9sw0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14201",
  "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.stat-mech"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "3104|Theoretical and Computational Physics"
    ]
  ],
  "openalex": "W7213250039",
  "pdf_url": "https://arxiv.org/pdf/2609.14201",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5j5s8t0rf9sw0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.14201",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14201"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Correlation comparisons and critical curves for disordered XY models",
  "title_text": "Correlation comparisons and critical curves for disordered XY models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/5j5s8t0rf9sw0",
  "venue": "arXiv",
  "versions": []
}