Comment on "A Kac-potential treatment of nonintegrable interactions" by Vollmayr-Lee and Luijten

Abstract

We comment the recent manuscript by Vollmayr-Lee and Luijten [cond-mat/0009031] focusing on classical systems with nonintegrable interactions. The authors claim that they have proved that Boltzmann-Gibbs statistics suffices for describing the system in thermal equilibrium. We show that this statement is a misleading oversimplification since it only applies for the $\lim_{N \to \infty} \lim_{t \to \infty}$ ordering, but certainly not for the $\lim_{t \to \infty} \lim_{N \to \infty}$ one. The latter can even be the {\it unique} physically meaningful situation for thermodynamically large systems.