Electromagnetic instability of the Thomson problemJ. De Luca1, S. B. Rodrigues2 and Y. Levin3
1 Departamento de Física, Universidade Federal de São Carlos Rod. Washington Luiz km 235, 13565-905, Caixa Postal 676, São Carlos, SP, Brazil
2 Departamento de Matemática, Universidade Federal de São Carlos Rod. Washington Luiz km 235, 13565-905, Caixa Postal 676, São Carlos, SP, Brazil
3 Instituto de Física, Universidade Federal do Rio Grande do Sul Caixa Postal 15051, CEP 91501-970, Porto Alegre, RS, Brazil
received 30 November 2004; accepted in final form 10 May 2005
published online 8 June 2005
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<nc(a), the ground state corresponds to a hexagonal Wigner crystal with a number of topological defects. However, if n>nc(a) the Wigner lattice is unstable with respect to small perturbations and the ground state becomes spontaneously magnetized for finite n.
64.60.Cn - Order-disorder transformations; statistical mechanics of model systems.
71.10.-w - Theories and models of many-electron systems.
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