Lowest-known Energy Configuration of $N=100000$ Coulomb Charges in a Disk: Breaking the $10^5$ Barrier

Abstract

We report the first calculation of the lowest-known energy configuration for $N=100000$ 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 $N=40886$ 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 $N=100000$ a single $24$-core CPU workstation without GPU acceleration required $\approx 31$ hours. The energy $E_{\min }=7.80466624157\times 10^9$ deviates from the asymptotic expansion fitted to $100\le N\le 5000$ data by only $2.525\times 10^{-7}$, providing a stringent test of its extrapolation to unprecedented scales. Bond-orientational order analysis reveals a polycrystalline bulk threaded by radial grain boundaries, establishing a new benchmark for two-dimensional Coulomb systems.

Article: 12 pages, 1 table; Supplemental Material: 6 pages, 6 figures, 1 table