Two-parametric fractional statistics models for anyons

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 nonextensive Polychronakos statistics and both the incomplete and the nonextensive 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 $\alpha\in[0;1]$, unlike the nonextensive 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.