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Defect free global minima in Thomson's problem of charges on a sphere

Eric Lewin Altschuler·Antonio Perez-Garrido
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Abstract

Given $N$ unit points charges on the surface of a unit conducting sphere, what configuration of charges minimizes the Coulombic energy $\sum_{i>j=1}^N 1/r_{ij}$? Due to an exponential rise in good local minima, finding global minima for this problem, or even approaches to do so has proven extremely difficult. For \hbox{$N = 10(h^2+hk+k^2)+ 2$} recent theoretical work based on elasticity theory, and subsequent numerical work has shown, that for $N \sim >500$--1000 adding dislocation defects to a symmetric icosadeltahedral lattice lowers the energy. Here we show that in fact this approach holds for all $N$, and we give a complete or near complete catalogue of defect free global minima.

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Eric Lewin Altschuler, Antonio Perez-Garrido. 2005-09-28. Defect free global minima in Thomson's problem of charges on a sphere. https://doi.org/10.1103/physreve.73.036108

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