{
  "abstract": "We study the $d$-dimensional generalization of Models II ($d=2$) and V ($d=3$) for liquid crystals introduced by Heilmann--Lieb (1979), which consists of dimers on the hypercubic lattice at chemical potential $μ$, interacting via a hard-core repulsion and a lateral attraction between parallel dimers with coupling constant $b>0$. For $d\\in\\{2,3\\}$, these models were conjectured to exhibit liquid-crystalline order at low temperatures provided that $μ+2(d-1)b>0$. We establish nematic order for all $d\\ge 2$ under the additional condition $(4d-6)b>μ$, which corresponds to the physical regime in which misaligned dimers are rare on scales comparable to the correlation length of the one-dimensional reference system. While the treatment of orientational order here follows the approach of our recent work on Model I, the proof of the absence of translational order relies on a custom implementation of cluster swapping in the sense of Sheffield (2005). Consequently, we deduce uniqueness of Gibbs measure and anisotropic exponential decay of correlations within each oriented phase.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08600",
  "author_total": 1,
  "authors": [
    {
      "name": "Qidong He"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3b5mx34fhjj0r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08600",
  "fulltext_url": null,
  "id": "3b5mx34fhjj0r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08600",
  "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.soft"
    ],
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "3104|Theoretical and Computational Physics"
    ]
  ],
  "openalex": "W7220996196",
  "pdf_url": "https://arxiv.org/pdf/2610.08600",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3b5mx34fhjj0r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.08600",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08600"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.soft",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Nematic order in monomer-dimer models of Heilmann and Lieb with lateral attraction in dimensions $d\\ge 2$",
  "title_text": "Nematic order in monomer-dimer models of Heilmann and Lieb with lateral attraction in dimensions d≥ 2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/3b5mx34fhjj0r",
  "venue": "arXiv",
  "versions": []
}