B. Bergersen et al., EQUILIBRIUM-CONFIGURATIONS OF PARTICLES ON A SPHERE - THE CASE OF LOGARITHMIC INTERACTIONS, Journal of physics. A, mathematical and general, 27(7), 1994, pp. 2579-2586
We consider a system of N particles which are confined to the surface
of a sphere and which interact via a potential that depends logarithmi
cally on their separation. The ground-state properties of this system
are investigated for N = 2 to 65. Unlike the case of Coulomb interacti
ons this system has ground-state configurations with zero dipole momen
t for all N. The thermal properties of a selected set of systems in th
e range N = 2 to 500 are determined by Monte Carlo simulation. The res
ults are compared with analytical calculations in the small- and large
-N limits.