A note on exclusion statistics parameter and Hausdorff dimension

TL;DR

This paper establishes a relationship between exclusion statistics parameter and Hausdorff dimension for an anyon gas at high temperature, classifying excitations into classes with shared virial coefficients.

Contribution

It introduces a novel relation between exclusion statistics parameter and Hausdorff dimension, providing a classification scheme for anyonic excitations.

Findings

Derived the relation g=h(2-h) for anyon gas

Classified anyonic excitations into classes labeled by Hausdorff dimension

Connected the exclusion statistics parameter to the second virial coefficient

Abstract

We obtain for an anyon gas in the high temperature limit a relation between the exclusion statistics parameter $g$ and the Hausdorff dimension $h$, given by $g=h(2-h)$. The anyonic excitations are classified into equivalence classes labeled by Hausdorff dimension, $h$, and in that limit, the parameter $g$ give us the second virial coefficient for any statistics, $\nu$. The anyonic excitations into the same class $h$ get the same value of this virial coefficient.