{
  "abstract": "We report the first calculation of the lowest-known energy configuration for $N=100\\,000$ classical point charges confined to a disk and interacting via the $1/r$ Coulomb potential - a system size never before achieved for the Thomson problem in a disk, more than doubling the previous record of $N=40\\,886$ reported by Amore and Zarate. An adaptive defect-targeting subdomain optimization strategy yields an approximately linear growth of the wall-clock time per cycle with $N$; for $N=100\\,000$ a single $24$-core CPU workstation without GPU acceleration required $\\approx31$ hours. The energy $E_{\\min}=7.80466624157\\times10^{9}$ deviates from the standard empirical asymptotic expansion by only $2.525\\times10^{-7}$. We demonstrate that this remarkable agreement provides a stringent test of the rigorous next-order asymptotic theory for Riesz interactions, while the residual deviation is consistent with an $O(N^{4/3})$ boundary-layer correction whose absence from the standard fitting basis biases the empirical $N^{3/2}$ coefficient away from its exact crystalline value, thereby tying the deviation to the two-dimensional crystallization conjecture. Bond-orientational order analysis reveals a polycrystalline bulk threaded by radial grain boundaries, establishing a new benchmark for two-dimensional Coulomb systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24722",
  "author_total": 2,
  "authors": [
    {
      "name": "Georgiy K. Lavrov"
    },
    {
      "name": "Eduard G. Nikonov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/am2bmy02grt3v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24722",
  "fulltext_url": null,
  "id": "am2bmy02grt3v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24722",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "physics.class-ph"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "openalex",
      "2612|Mathematical Approximation and Integration"
    ]
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  "openalex": "W7214005474",
  "pdf_url": "https://arxiv.org/pdf/2609.24722",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/am2bmy02grt3v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.24722",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24722"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Lowest-known Energy Configuration of $N=100\\,000$ Coulomb Charges in a Disk: Breaking the $10^{5}$ Barrier",
  "title_text": "Lowest-known Energy Configuration of N=100 000 Coulomb Charges in a Disk: Breaking the 10^5 Barrier",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/am2bmy02grt3v",
  "venue": "arXiv",
  "versions": []
}