Cirto, LJL; Rodriguez, A; Nobre, FD; Tsallis, C
The dynamics and thermostatistics of a classical inertial XY model, characterized by long-range interactions, are investigated on d-dimensional lattices (d = 1, 2, and 3), through molecular dynamics. The interactions between rotators decay with the distance r(ij) like 1/rij(alpha) (alpha >= 0), where alpha -> infinity and alpha = 0 respectively correspond to the nearest-neighbor and infinite-range interactions. We verify that the momenta probability distributions are Maxwellians in the short-range regime, whereas q-Gaussians emerge in the long-range regime. Moreover, in this latter regime, the individual energy probability distributions are characterized by long tails, corresponding to q-exponential functions. The present investigation strongly indicates that, in the long-range regime, central properties fall out of the scope of Boltzmann-Gibbs statistical mechanics, depending on d and alpha through the ratio alpha/d.