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A Kac-potential treatment of nonintegrable interactions

Benjamin P. Vollmayr-Lee·Erik Luijten
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Abstract

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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Benjamin P. Vollmayr-Lee, Erik Luijten. 2000-09-03. A Kac-potential treatment of nonintegrable interactions. https://doi.org/10.1103/physreve.63.031108

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