6533b82cfe1ef96bd128ff00

RESEARCH PRODUCT

Kac-potential treatment of nonintegrable interactions.

Erik LuijtenBenjamin Vollmayr-leeBenjamin Vollmayr-lee

subject

PhysicsClass (set theory)Statistical Mechanics (cond-mat.stat-mech)FOS: Physical sciencesContext (language use)Statistical mechanicsClassical mechanicsCutoffPeriodic boundary conditionsPairwise comparisonBoundary value problemStatistical physicsCondensed Matter - Statistical MechanicsInteraction range

description

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.

10.1103/physreve.63.031108https://pubmed.ncbi.nlm.nih.gov/11308631