Eur. Phys. J. B (2014) 87: 175
https://doi.org/10.1140/epjb/e2014-50171-8

Regular Article

Two-parametric fractional statistics models for anyons

Department for Theoretical Physics, Ivan Franko National University of Lviv, 12 Drahomanov St., 79005 Lviv, Ukraine

^a e-mail: andrij.rovenchak@gmail.com

Received: 13 March 2014
Received in final form: 6 May 2014
Published online: 1 August 2014

Abstract

In the paper, two-parametric models of fractional statistics are proposed in order to determine the functional form of the distribution function of free anyons. From the expressions of the second and third virial coefficients, an approximate correspondence is shown to hold for three models, namely, the nonadditive Polychronakos statistics and both the incomplete and the nonadditive modifications of the Haldane-Wu statistics. The difference occurs only in the fourth virial coefficient leading to a small correction in the equation of state. For the two generalizations of the Haldane-Wu statistics, the solutions for the statistics parameters g,q exist in the whole domain of the anyonic parameter α ∈ [0; 1], unlike the nonadditive Polychronakos statistics. It is suggested that the search for the expression of the anyonic distribution function should be made within some modifications of the Haldane-Wu statistics.