Comment to "Thomson rings in a disk"

TL;DR

This paper challenges previous findings on the lowest energy arrangements of charges in a disk, showing that configurations with defects near the center are energetically more favorable than the previously predicted hexagonal core and rings.

Contribution

It provides numerical evidence that the previously proposed centered configurations are not the true global minima for Coulomb charges in a disk.

Findings

Identified lower energy configurations with central defects.

Disproved the predicted hexagonal core and ring structures.

Showed that previous models are not reliable for guiding numerical searches.

Abstract

We have found that the minimum energy configuration of $N=395$ charges confined in a disk and interacting via the Coulomb potential, reported by Cerkaski et al. in Ref.~\cite{Cerkaski15} is not a global minimum of the total electrostatic energy. We have identified a large number of configurations with lower energy, where defects are present close to the center of the disk; thus, the formation of a hexagonal core and valence circular rings for the centered configurations, predicted by the model of Ref.~\cite{Cerkaski15}, is not supported by numerical evidence and the configurations obtained with this model cannot be used as a guide for the numerical calculations, as claimed by the authors.