Kac-potential treatment of nonintegrable interactions

We consider d-dimensional systems with nonintegrable, algebraically decaying pairwise interactions. It is shown that, upon the introduction of periodic boundary conditions and a long-distance cutoff in the interaction range, the bulk thermodynamics can be obtained rigorously by means of a Kac-potential treatment, leading to an exact, mean-field-like theory. This explains various numerical results recently obtained for finite systems in the context of “nonextensive thermodynamics,” and in passing exposes a strong regulator dependence not discussed in these studies. Our findings imply that, contrary to some claims, Boltzmann-Gibbs statistics are sufficient for a standard description of this class of nonintegrable interactions.