Influence of Dislocations in Thomson's Problem

Abstract

We investigate Thomson's problem of charges on a sphere as an example of a system with complex interactions. Assuming certain symmetries we can work with a larger number of charges than before. We found that, when the number of charges is large enough, the lowest energy states are not those with the highest symmetry. As predicted previously by Dodgson and Moore, the complex patterns in these states involve dislocation defects which screen the strains of the twelve disclinations required to satisfy Euler's theorem.