{
  "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 $C(r)\\sim r^{-2}$. The correlation and Binder ratios are nearly size independent at low temperature and collapse with the BKT-type variable $(T-T_{\\rm BKT})(\\log L)^2$; finite-size effects set in around $T\\simeq0.35\\text{--}0.4$, consistent with $T_{\\rm BKT}\\simeq0.35$. 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": [],
  "article_type": "Journal reference: Mathematics, 14, 3647 (2026)",
  "arxiv": "2609.00721",
  "author_total": 2,
  "authors": [
    {
      "name": "Hitomi Endo"
    },
    {
      "name": "Michikazu Kobayashi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/63q70f16kz1nr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00721",
  "fulltext_url": null,
  "id": "63q70f16kz1nr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00721",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.00721",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/63q70f16kz1nr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:11Z",
      "native_id": "2609.00721",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00721"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "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": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/63q70f16kz1nr",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.3390/math14203647",
      "pid": "ah2qfb5hvg3g3",
      "relation": "published-as",
      "title": "BKT-like Correlation Scaling and Twist Responses in a One-Dimensional Fractional U(1) Ginzburg–Landau Model",
      "venue": "Mathematics"
    }
  ]
}