{
  "abstract": "We study finite-state approximations to a chiral nematic lattice model whose local directors are embedded in three-dimensional orientational space. The model analyzed here is formulated in terms of a rotated quadrupolar interaction, which provides a direct angular chirality parameter $Δ$ and reduces to the usual planar chiral-nematic form for directors confined to the xy plane. On a rooted Cayley tree, the statistical problem is written as a nonlinear recursion for branch partition functions. In the infinite-coordination limit, with $rJ_Q$ fixed, the recursion becomes a softmax map for the state probabilities. We analyze Cartesian three-state, planar four-state, and non-planar four-state discretizations. The first supports ordered and period-two attractors, whereas the planar four-state discretization displays a sequence of commensurate and longer-period modulated attractors. Its disordered fixed point loses stability at $t=9/16$ through a complex-conjugate pair with phase $q=\\pm 2Δ$, so a modulated critical mode is selected for every nonzero chirality. The non-planar four-state set is intrinsically anisotropic and, when the stated model is reconstructed directly, supports prominent period-three as well as period-two and higher-period cycles. Because attractor stability does not by itself establish global thermodynamic stability, the diagrams reported here are interpreted as attractor/stability diagrams rather than equilibrium phase diagrams.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15891",
  "author_total": 1,
  "authors": [
    {
      "name": "William de Castilho"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/99rrbxqs0ytqv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15891",
  "fulltext_url": null,
  "id": "99rrbxqs0ytqv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15891",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "openalex",
      "3104|Theoretical and Computational Physics"
    ]
  ],
  "openalex": "W7213316190",
  "pdf_url": "https://arxiv.org/pdf/2609.15891",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/99rrbxqs0ytqv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.15891",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15891"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Modulated structures in discrete approximations to a three-dimensional cholesteric model on a recursive lattice",
  "title_text": "Modulated structures in discrete approximations to a three-dimensional cholesteric model on a recursive lattice",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:25Z",
  "url": "https://research.draconitic.com/paper/99rrbxqs0ytqv",
  "venue": "arXiv",
  "versions": []
}