MANY-PARTICLE JUMPS ALGORITHM AND THOMSONS PROBLEM

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.