Journal of Physics A Mathematical and General

Statistical aspects of the anyon model

Alain Comtet, Y Georgelin, Stéphane Ouvry

Published Sep 21, 1989• 85 citations

Abstract

The second virial coefficient for a gas of anyons is computed (i) by discretising the two-particle spectrum through the introduction of a harmonic potential regulator and (ii) by considering the problem in the continuum directly through heat kernel methods. In both cases the result of Arovas et al. (1985) is recovered.

DOI: 10.1088/0305-4470/22/18/026

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Journal of Physics A Mathematical and General

Statistical aspects of the anyon model

Alain Comtet, Y Georgelin, Stéphane Ouvry

Published Sep 21, 1989• 85 citations

Publisher

Abstract

DOI: 10.1088/0305-4470/22/18/026

Related papers

Second virial coefficient of the interacting anyon gas

Nikitas I. Gidopoulos, A. K. Theophilou

Arovas and co-workers, in their well-known paper on the statistical mechanics of anyons [D. P. Arovas, R. Schrieffer, F. Wilczek, and A. Zee, Nucl. Phys. B251, 117 (1985)], found that the second virial coefficient of a two-dimensional gas of free anyons exhibits nonanalytic behavior as the statistical parameter is varied in the neighborhood of the Bose point. In this paper we consider the anyons to be interacting, via a two-body interaction U(\ensuremath{\Vert} ${\mathbf{r}}_{1}$ - ${\mathbf{r}}_{2}$ \ensuremath{\Vert}), where ${\mathit{r}}^{2}$ U(r)\ensuremath{\rightarrow}0 as r\ensuremath{\rightarrow}0. Expanding the second virial coefficient in the vicinity of the Bose point, we show that the nonanalyticity is still present and independent of the particular form of U. Furthermore, we calculate explicitly, the second virial coefficient in the case of a short-range interaction.Arovas and co-workers, in their well-known paper on the statistical mechanics of anyons [D. P. Arovas, R. Schrieffer, F. Wilczek, and A. Zee, Nucl. Phys. B251, 117 (1985)], found that the second virial coefficient of a two-dimensional gas of free anyons exhibits nonanalytic behavior as the statistical parameter is varied in the neighborhood of the Bose point. In this paper we consider the anyons to be interacting, via a two-body interaction U(\ensuremath{\Vert}${\mathbf{r}}_{1}$-${\mathbf{r}}_{2}$\ensuremath{\Vert}), where ${\mathit{r}}^{2}$U(r)\ensuremath{\rightarrow}0 as r\ensuremath{\rightarrow}0. Expanding the second virial coefficient in the vicinity of the Bose point, we show that the nonanalyticity is still present and independent of the particular form of U. Furthermore, we calculate explicitly, the second virial coefficient in the case of a short-range interaction.

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{\mathbf{r}}_{1}

{\mathbf{r}}_{2}

\ensuremath{\Vert}), where

{\mathit{r}}^{2}

U(r)\ensuremath{\rightarrow}0 as r\ensuremath{\rightarrow}0. Expanding the second virial coefficient in the vicinity of the Bose point, we show that the nonanalyticity is still present and independent of the particular form of U. Furthermore, we calculate explicitly, the second virial coefficient in the case of a short-range interaction.

Evaluating the propagator by the usual time-sliced manner, we use it to compute the second virial coefficient of an anyon gas interacting through the repulsive potential of the form

g/r^2 (g > 0)

. All the cusps for the unpolarized spin-1/2 as well as spinless cases disappear in the

\\omega \\to 0

limit, where

\\omega

is a frequency of harmonic oscillator which is introduced as a regularization method. As

g

approaches to zero, the result reduces to the noninteracting hard-core limit.

We consider the statistical mechanics of an interacting anyon gas with a repulsive pair potential of the form g/

{\mathit{r}}^{2}

. The second virial coefficient is calculated and shown to be a smooth function of the statistical parameter \ensuremath{\alpha} for g>0, without the cusps previously found at the Bose point in a noninteracting anyon gas. As g\ensuremath{\rightarrow}0 the cusps remain absent but a different type of singularity develops at the Bose point, showing that the order of limits is crucial.