{
  "abstract": "We introduce a bootstrap method for deriving bounds on disorder-averaged observables in classical statistical systems with quenched disorder. The three main ingredients of the bootstrap are the positivity of ensembles of probability measures, disorder-averaged equations of motion, and explicit expectation values of random coupling variables. Together, these ingredients lead to a linear programming problem over the space of disorder averages. By further employing the positivity of the two-replica Gram matrix, we also formulate a semidefinite programming problem that produces bounds on two-replica correlators. We demonstrate the method using two examples: the two-dimensional random site-diluted Ising model and the one-dimensional disordered contact process. For the latter example, the bootstrap bounds exhibit a region of multiple kinks that we relate to the Griffiths region, whose finite-size scaling analysis yields a typical correlation length exponent in good numerical agreement with the known value.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20927",
  "author_total": 4,
  "authors": [
    {
      "name": "Minjae Cho"
    },
    {
      "name": "Yaprak Önder"
    },
    {
      "name": "Eslam Khalaf"
    },
    {
      "name": "Michael G. Scheer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0nyb6jkt21d74.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20927",
  "fulltext_url": null,
  "id": "0nyb6jkt21d74",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20927",
  "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",
      "hep-th"
    ],
    [
      "openalex",
      "3104|Theoretical and Computational Physics"
    ]
  ],
  "openalex": "W7213927621",
  "pdf_url": "https://arxiv.org/pdf/2609.20927",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0nyb6jkt21d74.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:03Z",
      "native_id": "2609.20927",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20927"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Bootstrapping Classical Systems with Quenched Disorder",
  "title_text": "Bootstrapping Classical Systems with Quenched Disorder",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:03Z",
  "url": "https://research.draconitic.com/paper/0nyb6jkt21d74",
  "venue": "arXiv",
  "versions": []
}