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Researchers have discovered improved configurations for the Thomson problem, which involves finding the lowest-energy arrangement of electrically repulsive charges confined to a disk. Using a combination of quenched molecular dynamics and a fixed-border technique, they identified new global minimum energy states for systems containing 60, 61, 92, and 99 charges that improve upon all previously known solutions. The new configuration for 92 charges exhibits clearer symmetry patterns than earlier solutions, and results were reproducible across multiple independent computational runs.
Why it matters
This work advances our understanding of charged particle arrangements in confined geometries, which has applications in colloidal science, materials design, and understanding defect patterns in two-dimensional systems. The computational methods developed could be applied to optimize other many-body problems in physics and chemistry.
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⚠️ Preprint – Noch nicht peer-reviewed
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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 $E_{mathrm{QMD}}(60)=2159.3584240930$, $E_{mathrm{QMD}}(61)=2237.19264190$, $E_{mathrm{QMD}}(92)=5358.35353314$, and $E_{mathrm{QMD}}(99)=6254.83029083$, 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.