Abstract

This work presents a possible way to study the long-range interacting particles in finite-infinite (mesoscopic-macroscopic) systems with periodic boundary conditions. A symmetric lattice and their contributions over all space are used in the problem. In the present model, we assume that at long distances, the two-body attractive potential decays as a 1/r(alpha) law. We verified that the potential in any particle converges (diverges) when the interactions are short(long)-ranged. On the other hand, forces in any particle converge rapidly in all cases. However, we adopt a nonextensive scaling and we guarantee that the potential converges anywhere.