Lowest-known Energy Configuration of N=100 000 Coulomb Charges in a Disk: Breaking the 105 Barrier
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 ≈31 hours. The energy Emin=7.80466624157×109 deviates from the standard empirical asymptotic expansion by only 2.525×10−7. 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(N4/3) boundary-layer correction whose absence from the standard fitting basis biases the empirical N3/2 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.
Related
- Breaking the Infinite Barrier in the 1/3--2/3 Conjecture
- Breaking the Shot-Noise Barrier: Cached Recycled Variance-Reduced Gradients for Quantum Optimization
- Breaking the Exponential Barrier: The First Polynomial-Time Algorithm for the Győri-Lovász Theorem
- Harmonic maps from spheres with lowest possible index and their properties
- New GAPN functions with the lowest possible algebraic degree
BibTeX
@misc{lavrov2026lowestknown,
title = {{Lowest-known Energy Configuration of $N=100\,000$ Coulomb Charges in a Disk: Breaking the $10^5$ Barrier}},
author = {Georgiy K. Lavrov and Eduard G. Nikonov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24722},
eprint = {2609.24722},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24722},
}
RIS
TY - UNPB
TI - Lowest-known Energy Configuration of N=100 000 Coulomb Charges in a Disk: Breaking the 10^5 Barrier
AU - Georgiy K. Lavrov
AU - Eduard G. Nikonov
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.24722
UR - https://arxiv.org/abs/2609.24722
AB - 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 ≈31 hours. The energy E_min=7.80466624157×10^9 deviates from the standard empirical asymptotic expansion by only 2.525×10^−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.
ER -