{
  "abstract": "We investigate the phase diagram and critical properties of the two-dimensional classical XY model with interactions decaying as $1/r^{2+σ}$. At the marginal case $σ=2$, we show that the low-temperature phase is characterized by logarithmic quasi-long-range order (log-QLRO), where spin correlations decay as a power of the logarithm of distance, $C(r)\\sim(\\ln r)^{-η_\\ell}$ with $η_\\ell\\propto T$, and that the transition into this phase is a continuous transition beyond both the Ginzburg-Landau-Wilson paradigm and the Berezinskii-Kosterlitz-Thouless mechanism. Our analysis combines a near-exact Gaussian spin-wave theory, an adiabatic renormalization-group analysis, and large-scale Monte Carlo simulations. We find that the $1/r^4$ interaction logarithmically modifies the spin-wave stiffness kernel as $γ(k)\\simeqκk^2\\ln(1/k)$, which suppresses vortex proliferation and gives rise to a nonuniversal correlation-length exponent $ν\\propto1/\\sqrt{2πκ}$. Crucially, our simulations reveal that the short-range algebraic QLRO phase is unstable against a weak long-range perturbation for $σ\\le2$. These results establish $σ=2$ as the crossover boundary between the long-range and short-range universality classes and provide a critical evaluation of recent theoretical proposals.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39267",
  "author_total": 3,
  "authors": [
    {
      "name": "Xianzhi Pan"
    },
    {
      "name": "Zhijie Fan"
    },
    {
      "name": "Youjin Deng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7ernc4scwpd4g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39267",
  "fulltext_url": null,
  "id": "7ernc4scwpd4g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39267",
  "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"
    ],
    [
      "openalex",
      "3104|Theoretical and Computational Physics"
    ]
  ],
  "openalex": "W7215035226",
  "pdf_url": "https://arxiv.org/pdf/2609.39267",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7ernc4scwpd4g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39267",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39267"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Logarithmic Quasi-Long-Range Order and Novel Continuous Phase Transition in the Two-Dimensional $XY$ Model with $1/r^4$ Interaction",
  "title_text": "Logarithmic Quasi-Long-Range Order and Novel Continuous Phase Transition in the Two-Dimensional XY Model with 1/r^4 Interaction",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/7ernc4scwpd4g",
  "venue": "arXiv",
  "versions": []
}