Many-particle jumps algorithm and Thomson's problem

We study Thomson's problem using a new numerical algorithm, valid for any interacting complex system based on the consideration of simultaneous many-particle transitions to reduce the characteristic slowing down 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 , and study the stability of the ground state as a function of the number of charges considered. We associate this stability with how well defined are the charges surrounded by five nearest neighbours, whose number always seems to be equal to 12.