{
  "abstract": "Shannon-R\\'enyi entropies extract universal information from the full measurement distribution of a quantum many-body state and have recently become experimentally accessible probes of conformal data. Yet their microscopic evaluation remains difficult even in exactly solvable free-fermion systems. We show that the Born distribution of the critical transverse-field Ising chain is exactly the parity boundary of a weak inverse-square classical Ising model, a structure revealed by the Cauchy form of its probability kernel. The construction is exact at finite size for every real $n>0$ and isolates the long-distance sectors controlling the $n>1$ thermodynamics. Cutting a finite interval generates the universal $c\\,n/[8(n-1)]$ logarithm directly from the missing $1/r^2$ interactions, with $c=1/2$ the Ising central charge. On the ring, the explicit finite-size factor has no constant term, while any additional noninteger singularity is confined to a residual cycle-only free energy. All explicit long-distance contributions become marginal only at $n=1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27909",
  "author_total": 1,
  "authors": [
    {
      "name": "Mohammad Ali Rajabpour"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0zvgwr029t11j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27909",
  "fulltext_url": null,
  "id": "0zvgwr029t11j",
  "issns": [],
  "landing_url": "https://hal.science/hal-05733389v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "0.phys"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05733389/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0zvgwr029t11j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:24Z",
      "native_id": "hal-05733389",
      "source": "hal",
      "url": "https://hal.science/hal-05733389v1"
    },
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2609.27909",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27909"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Microscopic Origin of the Shannon-Rényi Boundary Phase in the Critical Ising Chain",
  "title_text": "Microscopic Origin of the Shannon-Rényi Boundary Phase in the Critical Ising Chain",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:56Z",
  "url": "https://research.draconitic.com/paper/0zvgwr029t11j",
  "venue": "HAL",
  "versions": []
}