{
  "abstract": "For the nearest-neighbour Edwards--Anderson Ising model on the discrete torus, we prove existence of the quenched thermodynamic limit and almost-sure self-averaging of the free-energy density. The only moment assumption in the main argument is $\\E|J|<\\infty$, and no symmetry or centering of the coupling law is needed. The proof avoids periodic subadditivity: the wrap-around bonds form a surface-order perturbation, while a tiling argument and the strong law of large numbers give the free-boundary limit. We also obtain the quantitative bounds $(O(L^{-1})$ for the disorder-averaged finite-volume correction. A precise common probability space is specified, since an almost-sure statement across volumes is otherwise not well defined.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19005",
  "author_total": 3,
  "authors": [
    {
      "name": "Hexiang Wang"
    },
    {
      "name": "Keheng Zhu"
    },
    {
      "name": "Mauris Chueng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2231z21nrdhf7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19005",
  "fulltext_url": null,
  "id": "2231z21nrdhf7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19005",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "3104|Theoretical and Computational Physics"
    ]
  ],
  "openalex": "W7213502723",
  "pdf_url": "https://arxiv.org/pdf/2609.19005",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2231z21nrdhf7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:01Z",
      "native_id": "2609.19005",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19005"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The Thermodynamic Limit of Short-Range Spin Glasses with Periodic Boundary Conditions",
  "title_text": "The Thermodynamic Limit of Short-Range Spin Glasses with Periodic Boundary Conditions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/2231z21nrdhf7",
  "venue": "arXiv",
  "versions": []
}