{
  "abstract": "We study the one-dimensional long-range self-avoiding walk in the grand-canonical ensemble where the statistical weight of a jump of length $r$ decays algebraically as $r^{-(d+σ)}$. Using large-scale Monte Carlo simulations with an efficient irreversible update scheme, we obtain high-precision estimates of the critical fugacity $z_c$, the universal Binder ratio $Q_N^c$, the correlation-length exponent $ν$, and the anomalous dimension $η$. For $σ>1$, the critical fugacity varies smoothly with $σ$, while the Binder ratio and the critical exponents remain consistent with the short-range universality class. For $σ\\le 1$, by contrast, the results clearly depart from short-range behavior, identifying $σ=1$ as the boundary between long-range and short-range regimes. In the long-range Wilson-Fisher regime with $1/2 < σ\\leq 1$, $η$ agrees with the long-range Gaussian-fixed-point prediction $η_{\\mathrm{GFP}}=2-σ$, whereas $Q_N^c$ and $ν$ vary nontrivially with $σ$ and exhibit discontinuous jumps at $σ=1$. These findings are in good agreement with the recently proposed universality diagram in the $(d,σ)$ plane for long-range O$(n)$ models, with the self-avoiding walk corresponding to the $n\\to0$ limit.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23346",
  "author_total": 5,
  "authors": [
    {
      "name": "Jiang Zhou"
    },
    {
      "name": "Ziyu Liu"
    },
    {
      "name": "Pengcheng Hou"
    },
    {
      "name": "Zhijie Fan"
    },
    {
      "name": "Youjin Deng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3bzxkvpsgjpr2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23346",
  "fulltext_url": null,
  "id": "3bzxkvpsgjpr2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23346",
  "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",
      "3104|Theoretical and Computational Physics"
    ]
  ],
  "openalex": "W7213996006",
  "pdf_url": "https://arxiv.org/pdf/2609.23346",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3bzxkvpsgjpr2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.23346",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23346"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Long-range self-avoiding walk in one dimension: a Monte Carlo study",
  "title_text": "Long-range self-avoiding walk in one dimension: a Monte Carlo study",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:19Z",
  "url": "https://research.draconitic.com/paper/3bzxkvpsgjpr2",
  "venue": "arXiv",
  "versions": []
}