{
  "abstract": "We introduce a random matrix framework for studying statistical-mechanical lattice systems through spectral observables. Equilibrium configurations sampled from a Boltzmann measure are mapped to matrix ensembles whose covariance structure is inherited from the spatial correlations of the underlying model. This construction maps real-space correlation functions to a momentum-space variance profile, providing a direct bridge between statistical-mechanical correlations and correlated random matrix ensembles. We derive this variance profile in finite-correlation-length and critical regimes, and compute spectral moments within a Wick-contraction expansion. A complementary self-consistent description of the bulk density is developed using the resolvent formalism. These analytical methods are benchmarked against Monte Carlo data for the two-dimensional Ising model and three-dimensional Edwards--Anderson spin glasses. In both cases, the spectra evolve from the semicircle law at high temperature to model-dependent critical forms reflecting the structure of correlations. The framework, therefore, provides a quantitative spectral route to probing collective behavior in ordered and disordered statistical systems, while also defining a class of physically motivated correlated random matrix ensembles.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Phys. Rev. B 114, 204203 (2026)",
  "arxiv": "2605.21254",
  "author_total": 3,
  "authors": [
    {
      "name": "Yaprak Önder"
    },
    {
      "name": "Abbas Ali Saberi"
    },
    {
      "name": "Roderich Moessner"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/650jhwh4mntwy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.21254",
  "fulltext_url": null,
  "id": "650jhwh4mntwy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.21254",
  "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",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "math-ph"
    ],
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      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "physics.data-an"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2605.21254",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/650jhwh4mntwy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2605.21254",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.21254"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.data-an",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Random Matrix Spectra from Boltzmann-Weighted Lattice Ensembles",
  "title_text": "Random Matrix Spectra from Boltzmann-Weighted Lattice Ensembles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/650jhwh4mntwy",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1103/5xm2-81c1",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}