{
  "abstract": "We perform large-scale numerical simulations to investigate the critical behavior of $k$-core percolation in two dimensions with an extended interaction range $r$. By systematically varying both the core index $k$ and the interaction range $r$, we construct a comprehensive phase diagram in the $(k,r)$ plane. In contrast to $k$-core percolation in infinite dimensions, no hybrid transition is observed in two dimensions: the phase diagram contains only a continuous transition regime and a strictly first-order regime, separated by a tricritical or critical-end point $(k_s,r_s)$. For $k<k_s$ and $r<r_s$, the transition is continuous and belongs to the universality class of standard two-dimensional (2D) percolation. For $k>k_s$ and finite $r>r_s$, the transition is discontinuous, with no hybrid features or critical singularities. In this first-order regime, the pseudocritical point approaches the critical point as $1/\\ln L$, where $L$ is the linear system size, distinct from the $L^{-d}$ scaling typical of conventional thermodynamic first-order transitions in $d$ dimensions. This logarithmic finite-size drift is consistent with a nucleation-driven mechanism, in which rare voids trigger the collapse of the finite-range $k$-core. These results demonstrate that geometric constraints can fundamentally alter the nature of $k$-core percolation found in finite dimensions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Physical Review E 114, 034103 (2026)",
  "arxiv": "2605.25812",
  "author_total": 3,
  "authors": [
    {
      "name": "Qiyuan Shi"
    },
    {
      "name": "Ming Li"
    },
    {
      "name": "Youjin Deng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/35b02fgz1v7z3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.25812",
  "fulltext_url": null,
  "id": "35b02fgz1v7z3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.25812",
  "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/2605.25812",
  "pmcid": null,
  "pmid": null,
  "published": "2026-05-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/35b02fgz1v7z3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:41Z",
      "native_id": "2605.25812",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.25812"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Equivalent-neighbor $k$-core percolation in two dimensions",
  "title_text": "Equivalent-neighbor k-core percolation in two dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:41Z",
  "url": "https://research.draconitic.com/paper/35b02fgz1v7z3",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1103/sbf3-yfl5",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}