The fourth virial coefficient of anyons

Details The fourth virial coefficient of anyons The fourth virial coefficient of anyons

1997-11-18

arxiv.org/abs/cond-mat/9711169v1

Physics

Condensed Matter

Statistical Mechanics

30 pages, 12 figures, LaTeX2e

Scientific paper

10.1142/S0217751X9800175X

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.

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