Cirto, L. J. L.,Assis, V. R. V.,Tsallis, C.

We numerically study a one-dimensional system of N classical localized planar rotators coupled through interactions which decay with distance as 1/r(alpha) (alpha >= 0). The approach is a first principle one (i.e., based on Newton's law), and yields the probability distribution of momenta. For alpha large enough and N >> 1 we observe, for longstanding states, the Maxwellian distribution, landmark of Boltzmann-Gibbs thermostatistics. But, for alpha small or comparable to unity, we observe instead robust fat-tailed distributions that are quite well fitted with q-Gaussians. These distributions extremize, under appropriate simple constraints, the nonadditive entropy S-q upon which nonextensive statistical mechanics is based. The whole scenario appears to be consistent with nonergodicity and with the thesis of the q-generalized Central Limit Theorem.