{"ID":23507438,"CreatedAt":"2026-09-18T02:21:44.056544415Z","UpdatedAt":"2026-09-20T18:11:56.143995915Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.20777","arxiv_id":"2609.20777","title":"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 $E_{\\mathrm{QMD}}(60)=2159.3584240930$, $E_{\\mathrm{QMD}}(61)=2237.19264190$, $E_{\\mathrm{QMD}}(92)=5358.35353314$, 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.","short_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 configuratio...","url_abs":"https://arxiv.org/abs/2609.20777","url_pdf":"https://arxiv.org/pdf/2609.20777v1","authors":"[\"Georgiy K. Lavrov\",\"Eduard G. Nikonov\"]","published":"2026-09-17T17:49:04Z","proceeding":"cond-mat.stat-mech","tasks":"[\"cond-mat.stat-mech\",\"math-ph\",\"math.OC\",\"physics.class-ph\",\"physics.comp-ph\"]","methods":"[]","has_code":false}