{
  "abstract": "Conditional mutual information (CMI) probes spatial non-Markovianity and plays a central role in a recently developed framework for defining mixed-state phases based on local reversibility. This framework sharply distinguishes exponentially decaying from algebraically decaying CMI, since the latter obstructs equivalence to a state with finite Markov length. Here we show that states that flow to the same renormalization-group (RG) fixed point can nevertheless exhibit qualitatively different CMI. Starting from a critical Gibbs state of a finite-range local classical Hamiltonian, whose CMI vanishes beyond the interaction range, we show that an RG-irrelevant perturbation that breaks detailed balance generically generates algebraically decaying CMI. Crucially, these power-law tails are cutoff-suppressed: although they lead to an infinite Markov length at every fixed lattice cutoff, they vanish as a positive power of the cutoff in the continuum limit. We construct solvable models that exhibit this phenomenon and predict that the Ising-symmetric critical point of Toom's cellular automata generically exhibits such behavior. We also find analogous cutoff-suppressed CMI in the high-temperature paramagnetic phase of the long-range Ising paramagnet, in contrast with the genuine power-law CMI at the finite-temperature critical point in this same model that survives the continuum limit. We also derive a general result that in one spatial dimension, CMI decays faster than the inverse square of the buffer length if and only if the long-distance physics is Markovian.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11235",
  "author_total": 2,
  "authors": [
    {
      "name": "Yu-Hsueh Chen"
    },
    {
      "name": "Tarun Grover"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dke8f1fwgjvta.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11235",
  "fulltext_url": null,
  "id": "dke8f1fwgjvta",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11235",
  "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",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7221068709",
  "pdf_url": "https://arxiv.org/pdf/2610.11235",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dke8f1fwgjvta.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:54Z",
      "native_id": "2610.11235",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11235"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Markov length can diverge in systems whose universal physics is spatially Markovian",
  "title_text": "Markov length can diverge in systems whose universal physics is spatially Markovian",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:54Z",
  "url": "https://research.draconitic.com/paper/dke8f1fwgjvta",
  "venue": "arXiv",
  "versions": []
}