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

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.

Revisions in Tables and References

References in corpus (8)

• Interacting Topological Defects on Frozen Topographies
• Crystalline Order on a Sphere and the Generalized Thomson Problem
• Influence of Dislocations in Thomson's Problem
• Vortices in a Thin Film Superconductor with a Spherical Geometry
• Symmetric patterns of dislocations in Thomson's problem
• Ground state of a large number of particles on a frozen topography
• Investigation on the Ground States of a Model Thin-Film Superconductor on a Sphere
• Electromagnetic instability of the Thomson Problem

Cited by in corpus (9)

• Experimental study of energy-minimizing point configurations on spheres
• Kinetic Transition Networks for the Thomson Problem and Smale's 7th Problem
• Interstitial Fractionalization and Spherical Crystallography
• Correspondences between the Classical Electrostatic Thomson Problem and Atomic Electronic Structure
• The most uniform distribution of points on the sphere
• Discrete Transformations in the Thomson Problem
• Charged particles constrained to a curved surface
• Some spherical codes in S2 and their algebraic numbers
• Slightly broken icosahedral symmetry advances Thomson problem