Kac-potential treatment of nonintegrable interactions

Benjamin P. Vollmayr-Lee, Erik Luijten*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


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.

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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