Comment on " Thermodynamics of a One- Dimensional Ideal Gas with fractional Exclusion Statistics "

TL;DR

This paper critiques a previous claim about the thermodynamics of a one-dimensional Calogero model, arguing that all virial coefficients depend on the statistical parameter when the thermodynamic limit is correctly applied.

Contribution

It clarifies that all virial coefficients are influenced by the statistical parameter in the Calogero model, correcting prior conclusions that only the second coefficient was affected.

Findings

All virial coefficients depend on the statistical parameter.

Proper thermodynamic limit alters previous results.

Challenges earlier claims about the model's thermodynamics.

Abstract

In a recent letter -Phys. Rev. Lett. 73, 3331 (1995)-, the conclusion was reached that, in the one-dimensional Calogero model, only the second virial coefficient is affected by the statistical parameter $\alpha$, where $\alpha$ is related to the coupling constant $\kappa/ x_{ij}^2$ of the Calogero interaction by $\kappa=\alpha(\alpha+1)$. We argue that it is not so, i.e. all virial coefficients are affected, if the thermodynamic limit is properly taken.