%0 Journal Article 
%A Altschuler, Eric Lewin
%A Pérez Garrido, Antonio
%T New global minima for Thomson´s problem of charges on a sphere
%D 2005
%@ 1550-2376
%U http://arxiv.org/abs/cond-mat/0408355
%U http://hdl.handle.net/10317/583
%X Using numerical arguments we find that for N = 306 a tetrahedral configuration (Th) and for N = 542 a dihedral configuration (D5) are likely the global energy minimum for Thomson’s problem of minimizing the energy of N unit charges on the surface of a unit conducting sphere. These would be the largest N by far, outside of the icosadeltahedral series, for which a global minimum for Thomson’s problem is known. We also note that the current theoretical understanding of Thomson’s problem does not rule out a symmetric configuration as the global minima for N = 306 and 542. We explicitly find that analogues of the tetrahedral and dihedral configurations for N larger than 306 and 542, respectively, are not global minima, thus helping to confirm the theory
of Dodgson and Moore (Phys. Rev. B 55, 3816 (1997)) that as N grows dislocation defects
can lower the lattice strain of symmetric configurations and concomitantly the energy. As well, making explicit previous work by ourselves and others, for N < 1000 we give a full accounting of icosadeltahedral configuration which are not global minima and those which appear to be, and
discuss how this listing and our results for the tetahedral and dihedral configurations may be used to refine theoretical understanding of Thomson’s problem.
%K Física Aplicada
%K Problema de Thomson
%K Configuración simétrica
%K Esferas
%K Estructuras esféricas
%~ GOEDOC, SUB GOETTINGEN