A Kac-potential treatment of nonintegrable interactions

Details A Kac-potential treatment of nonintegrable interactions A Kac-potential treatment of nonintegrable interactions

2000-09-03

arxiv.org/abs/cond-mat/0009031v1

Phys. Rev. E 63, 031108 (2001)

Physics

Condensed Matter

Statistical Mechanics

RevTeX, 8 pages, 1 figure

Scientific paper

10.1103/PhysRevE.63.031108

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.

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