Comment on ``Quantum Statistical Mechanics of an Ideal Gas with Fractional Exclusion Statistics in Arbitrary Dimension"

TL;DR

This paper critiques a previous claim about the factorization of anyon thermodynamic potential, showing it only holds in two-dimensional systems, thus clarifying the conditions under which fractional exclusion statistics can be separated.

Contribution

It corrects a prior assertion by demonstrating the specific dimensionality where thermodynamic quantities of anyon gases can be factorized.

Findings

Factorization of thermodynamic quantities only valid in 2D systems.

The proposed factorization relation does not hold in arbitrary dimensions.

Clarifies the limitations of fractional exclusion statistics in different dimensions.

Abstract

It is mentioned that anyon thermodynamic potential $Q(\alpha, N)$ could not be factorized in terms characteristic of the ideal boson $\alpha =0$ and fermion $\alpha =1$ gases by the relation $Q(\alpha, N) = (1-\alpha) Q(0, N_b)+ \alpha Q(1, N_f)$ in which $N=N_f +N_b$, that claimed in Phys. Rev. Lett. 78, 3233 (1997). Our analyses indicate that the thermodynamic quantities of anyon gas may be factorized as $Q(\alpha) = \alpha Q(1) + (1-\alpha) Q(0)$ only in the two-dimension system.