Kac-potential treatment of nonintegrable interactions - art. no. 031108

We consider d-dimensional systems with nonintegrable, algebraically decayin g pairwise interactions. It is shown that, upon the introduction of periodi c boundary conditions and a long-distance cutoff in the interaction range, the bulk thermodynamics can be obtained rigorously by means of a Kac-potent ial treatment, leading to an exact, mean-field-like theory. This explains V arious numerical results recently obtained for finite systems in the contex t of "nonextensive thermodynamics," and in passing exposes a strong regulat or dependence not discussed in these studies. Our findings imply that, cont rary to some claims, Boltzmann-Gibbs statistics are sufficient for a standa rd description of this class of nonintegrable interactions.