Global Minima of the Thomson Problem in a Disk: A Molecular Dynamics Approach with Fixed Border Charges
Abstract
We report improved global-minimum configurations for the classical Thomson problem of N=60, $61$, $92$, and $99$ repulsive Coulomb charges confined to a disk. By combining the quenched molecular dynamics (QMD) method with the fixed-border heuristic introduced by Amore and Zarate, we systematically obtain configurations with energies EQMD(60)=2159.3584240930, EQMD(61)=2237.19264190, EQMD(92)=5358.35353314, and EQMD(99)=6254.83029083, which improve upon the previously best-known values. For N=60, the Voronoi diagram of our configuration differs from the one reported earlier. The symmetries for N=61 (C2) and N=99 (D1) are confirmed and are consistent with the known symmetry patterns for these configurations. For N=92, whereas the previously reported Voronoi diagram has lower symmetry, our solution exhibits a clear D1 (axial) symmetry of defects. The results are highly reproducible across multiple independent runs, providing strong evidence that these configurations are robust global-minimum candidates.
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BibTeX
@misc{lavrov2026global,
title = {{Global Minima of the Thomson Problem in a Disk: A Molecular Dynamics Approach with Fixed Border Charges}},
author = {Georgiy K. Lavrov and Eduard G. Nikonov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20777},
eprint = {2609.20777},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20777},
}
RIS
TY - UNPB
TI - Global Minima of the Thomson Problem in a Disk: A Molecular Dynamics Approach with Fixed Border Charges
AU - Georgiy K. Lavrov
AU - Eduard G. Nikonov
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20777
UR - https://arxiv.org/abs/2609.20777
AB - We report improved global-minimum configurations for the classical Thomson problem of N=60, $61$, $92$, and $99$ repulsive Coulomb charges confined to a disk. By combining the quenched molecular dynamics (QMD) method with the fixed-border heuristic introduced by Amore and Zarate, we systematically obtain configurations with energies E_QMD(60)=2159.3584240930, E_QMD(61)=2237.19264190, E_QMD(92)=5358.35353314, and E_QMD(99)=6254.83029083, which improve upon the previously best-known values. For N=60, the Voronoi diagram of our configuration differs from the one reported earlier. The symmetries for N=61 (C_2) and N=99 (D_1) are confirmed and are consistent with the known symmetry patterns for these configurations. For N=92, whereas the previously reported Voronoi diagram has lower symmetry, our solution exhibits a clear D_1 (axial) symmetry of defects. The results are highly reproducible across multiple independent runs, providing strong evidence that these configurations are robust global-minimum candidates.
ER -