A. Perezgarrido et al., MANY-PARTICLE JUMPS ALGORITHM AND THOMSONS PROBLEM, Journal of physics. A, mathematical and general, 29(9), 1996, pp. 1973-1978
We study Thomson's problem using a new numerical algorithm, valid for
any interacting complex system based on the consideration of simultane
ous many-particle transitions to reduce the characteristic slowing dow
n of numerical algorithms when applied to critical or complex systems.
We improve or reproduce all previous results on the Thomson problem,
using much less computer time than the other numerical algorithms. We
report ground-state energies for 101 less than or equal to N less than
or equal to 135, and study the stability of the ground state as a fun
ction of the number of charges considered. We associate this stability
with how well defined are the charges surrounded by five nearest neig
hbours, whose number always seems to be equal to 12.