Kac-potential treatment of nonintegrable interactions

Benjamin P. Vollmayr-Lee and Erik Luijten
Phys. Rev. E 63, 031108 – Published 26 February 2001
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Abstract

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.

  • Received 3 September 2000

DOI:https://doi.org/10.1103/PhysRevE.63.031108

©2001 American Physical Society

Authors & Affiliations

Benjamin P. Vollmayr-Lee1,2 and Erik Luijten3,*

  • 1Department of Physics, Bucknell University, Lewisburg, Pennsylvania 17837
  • 2Institut für Physik, WA 331, Johannes Gutenberg-Universität, D-55099 Mainz, Germany
  • 3Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742-2431

  • *Permanent address.

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Issue

Vol. 63, Iss. 3 — March 2001

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