The third virial coefficient of anyons revisited

TL;DR

This paper presents a highly precise numerical calculation of the third virial coefficient for free anyons, revealing a small sinusoidal correction term and significantly improving upon previous Monte Carlo results.

Contribution

The authors developed an improved numerical method to accurately compute the third virial coefficient of anyons, correcting for truncation effects and achieving three orders of magnitude better precision.

Findings

Third virial coefficient calculated with high precision

Identification of a small sinusoidal correction term

Results significantly more accurate than previous Monte Carlo estimates

Abstract

We use the method of solving the three-anyon problem developed in our earlier publication to evaluate numerically the third virial coefficient of free anyons. In order to improve precision, we explicitly correct for truncation effects. The present calculation is about three orders of magnitude more precise than the previous Monte Carlo calculation and indicates the presence of a term $a sin^4 \pi\nu$ with a very small coefficient $a \simeq -1.65 10^{-5}$.