Electromagnetic instability of the Thomson Problem

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 $n$.

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