{
  "abstract": "We study a one-dimensional fractional U(1) Ginzburg–Landau model whose quadratic part has Fourier multiplier |k|σ, focusing on the marginal case σ=1. This dispersion yields logarithmic spin-wave fluctuations, suggesting BKT-like behavior despite the one-dimensional setting. We sample the equilibrium Gibbs measure using stochastic Gross–Pitaevskii dynamics and analyze correlation functions, dimensionless ratios, effective exponents, and twist responses. The correlation function shows a low-temperature algebraic branch with a temperature-dependent exponent, while the high-temperature regime exhibits a nonlocal-kernel-induced tail consistent with C(r)∼r−2. The correlation and Binder ratios are nearly size-independent at low temperature and collapse with the BKT-type variable (T−TBKT)(logL)2; finite-size effects set in around T≃0.35–0.4, consistent with TBKT≃0.35. Unlike the two-dimensional XY model, twist responses do not yield a finite helicity modulus: the ordinary linear-response quantity grows with system size, whereas the cusp twist response scales as L−η(T), like the squared zero-mode order parameter. Thus, the transition is BKT-like in correlation scaling, but lacks a universal helicity-modulus jump.",
  "abstract_shown": true,
  "affiliations": [
    "School of Engineering Science, Kochi University of Technology, Kochi 782-8502, Japan"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Hitomi Endo",
      "orcid": "0009-0006-6471-2201"
    },
    {
      "affs": [
        0
      ],
      "name": "Michikazu Kobayashi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ah2qfb5hvg3g3.bib",
  "cited_by": 0,
  "doi": "10.3390/math14203647",
  "fulltext_url": null,
  "id": "ah2qfb5hvg3g3",
  "issns": [
    "2227-7390"
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  "landing_url": "https://www.mdpi.com/2227-7390/14/20/3647",
  "language": null,
  "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": null,
  "native_subjects": [
    [
      "openalex",
      "3104|Theoretical and Computational Physics"
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  "openalex": "W7206205166",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/ah2qfb5hvg3g3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14203647",
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      "url": "https://www.mdpi.com/2227-7390/14/20/3647"
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  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3104|Theoretical and Computational Physics",
      "subfield": "condensed-matter"
    }
  ],
  "title": "BKT-like Correlation Scaling and Twist Responses in a One-Dimensional Fractional U(1) Ginzburg–Landau Model",
  "title_text": "BKT-like Correlation Scaling and Twist Responses in a One-Dimensional Fractional U(1) Ginzburg–Landau Model",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/ah2qfb5hvg3g3",
  "venue": "Mathematics",
  "versions": [
    {
      "doi": "10.48550/arxiv.2609.00721",
      "pid": "63q70f16kz1nr",
      "relation": "preprint",
      "title": "BKT-like Correlation Scaling and Twist Responses in a One-Dimensional Fractional $U(1)$ Ginzburg--Landau Model",
      "venue": "arXiv"
    }
  ]
}