{
  "abstract": "We study the two-dimensional XY model with the nonanalytic pair potential $2[(1-\\cosδ)/2]^{p}$, whose small-angle law $\\propto|δ|^{2p}$ carries a cusp for $p<1$ and a flat bottom for $p>1$, invalidating the harmonic spin-wave expansion. Two questions arise: the nature of the low-temperature ($T$) phase and of the phase transition. A naive energetic argument would predict genuine long-range order and an enhanced transition temperature for $p<1$, and no transition at all for $p>1$. Large-scale Monte Carlo simulations contradict both: for every $p>0$ the \\dengrevxxi{low-$T$ phase} is quasi-long-range ordered, with anomalous dimension $η(T)\\propto T^{1/p}$, and terminates at a Berezinskii--Kosterlitz--Thouless transition. Using a vortex-free noncompact lattice-field description and utilizing a duality transformation, we show that coarse-graining drives the height-difference distribution onto a single Gaussian fixed point, renormalizing the cusp and flatness into a finite harmonic stiffness that restores the spin-wave description and the BKT scenario for all $p>0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12560",
  "author_total": 5,
  "authors": [
    {
      "name": "Sihan Hu"
    },
    {
      "name": "Xianzhi Pan"
    },
    {
      "name": "Kun Chen"
    },
    {
      "name": "Yi Jiang"
    },
    {
      "name": "Youjin Deng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f131rpg1wespz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12560",
  "fulltext_url": null,
  "id": "f131rpg1wespz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12560",
  "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.stat-mech"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.12560",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f131rpg1wespz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:07Z",
      "native_id": "2609.12560",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12560"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Persistence of BKT phase transition in the 2D nonanalytic XY model",
  "title_text": "Persistence of BKT phase transition in the 2D nonanalytic XY model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:07Z",
  "url": "https://research.draconitic.com/paper/f131rpg1wespz",
  "venue": "arXiv",
  "versions": []
}