Communications in Theoretical Physics

Second Virial Coefficient of Anyons with Spins

Shun-Qing Shen, Jianming Cai, Ruibao Tao

Published Jul 1, 1992• 0 citations

Abstract

We study the statistical properties of a two-dimensional gas of free anyone with spin. The concept of spin carried by anyons has been discussed in detail based on the two-dimensional Dirac equation. The second virial coefficient for the gas is evaluated and is found that it is the result of Arovas et al.[1] but not the result of Blum et al.[2] that is recovered, which is periodical for the statistical parameter with the length .

DOI: 10.1088/0253-6102/18/1/27

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Communications in Theoretical Physics

Second Virial Coefficient of Anyons with Spins

Shun-Qing Shen, Jianming Cai, Ruibao Tao

Published Jul 1, 1992• 0 citations

Publisher

Abstract

DOI: 10.1088/0253-6102/18/1/27

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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Physical review. B, Condensed matterApr 15, 199614 citations

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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.

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.