发表机构
Dzhelepov Laboratory of Nuclear Problems, JINR; Dubna State University; Meshcheryakov Laboratory of Information Technologies, JINR; HSE University（杰列波夫核问题实验室; 杜布纳国立大学; 梅什恰里亚科夫信息技术实验室; 高等经济学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
我们首次计算了圆盘内十万个库仑电荷的最低能量构型，突破十万规模，采用自适应缺陷靶向子域优化，能量与渐近展开高度吻合，并揭示多晶结构，为二维库仑系统建立新基准。
AI 中文摘要
我们报告了首次计算 $N=100\\,000$ 个经典点电荷被限制在圆盘内并通过 $1/r$ 库仑势相互作用的已知最低能量构型——这是圆盘汤姆逊问题中从未达到过的系统规模，比 Amore 和 Zarate 报告的 $N=40\\,886$ 的先前记录增加了一倍多。一种自适应缺陷靶向子域优化策略使得每个周期的墙钟时间随 $N$ 近似线性增长；对于 $N=100\\,000$，一台无需 GPU 加速的 $24$ 核 CPU 工作站需要约 $31$ 小时。能量 $E_{\min}=7.80466624157\times10^{9}$ 与拟合 $100\le N\le5000$ 数据的渐近展开式的偏差仅为 $2.525\times10^{-7}$，为其外推到前所未有的规模提供了严格检验。键取向序分析揭示了由径向晶界穿过的多晶块体，为二维库仑系统建立了新的基准。
英文摘要
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.
CommentsArticle: 14 pages, 1 table; Supplemental Material: 6 pages, 6 figures, 1 table
