The fourth virial coefficient of anyons

TL;DR

This paper calculates the fourth virial coefficient of free anyons using Monte Carlo methods, providing a Fourier series fit and explicit polynomial approximations, and demonstrates the finiteness of all cluster and virial coefficients.

Contribution

It introduces a novel Monte Carlo approach to compute the fourth virial coefficient of anyons and provides explicit polynomial approximations for path integral contributions.

Findings

The fourth virial coefficient can be fitted by a four-term Fourier series.

All cluster and virial coefficients are finite.

Only the second virial coefficient depends on statistics.

Abstract

We have computed by a Monte Carlo method the fourth virial coefficient of free anyons, as a function of the statistics angle theta. It can be fitted by a four term Fourier series, in which two coefficients are fixed by the known perturbative results at the boson and fermion points. We compute partition functions by means of path integrals, which we represent diagrammatically in such a way that the connected diagrams give the cluster coefficients. This provides a general proof that all cluster and virial coefficients are finite. We give explicit polynomial approximations for all path integral contributions to all cluster coefficients, implying that only the second virial coefficient is statistics dependent, as is the case for two-dimensional exclusion statistics. The assumption leading to these approximations is that the tree diagrams dominate and factorize.