  We consider d-dimensional systems with nonintegrable, algebraically decaying
pairwise interactions. It is shown that, upon 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.
