Electromagnetic instability of the Thomson Problem

TL;DR

This paper investigates the stability of charged particles on a sphere under electromagnetic effects, revealing a transition from a crystalline to a magnetized state as particle number increases.

Contribution

It introduces an analysis of the Thomson problem incorporating electromagnetic interactions via the Darwin approximation, highlighting a new instability leading to spontaneous magnetization.

Findings

Wigner crystal forms for particle number below critical value

Wigner lattice becomes unstable and magnetized when particle number exceeds critical

Electromagnetic effects induce a phase transition in the system

Abstract

The classical Thomson problem of $n$ charged particles confined to the surface of a sphere of radius $a$ is analyzed within the Darwin approximation of electrodynamics. For $n<n_c(a)$ the ground state corresponds to a hexagonal Wigner crystal with a number of topological defects. However, if $n>n_c(a)$ the Wigner lattice is unstable with respect to small perturbations and the ground state becomes spontaneously magnetized for finite $n$.