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arXiv:hep-th/9710056 · Journal of Physics A Mathematical and General

The second virial coefficient of spin- interacting anyon system

Sahng-Kyoon Yoo, D K Park

Published Jan 1, 1999• 0 citations
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Abstract

We evaluate the propagator by the usual time-sliced manner and use it to compute the second virial coefficient of an anyon gas interacting through the repulsive potential of the form . All the cusps for the unpolarized spin- as well as spinless cases disappear in the limit, where is a frequency of the harmonic oscillator which is introduced as a regularization method. As g approaches zero, the result reduces to the noninteracting hard-core limit.

DOI
10.1088/0305-4470/32/6/006

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We evaluate the propagator by the usual time-sliced manner and use it to compute the second virial coefficient of an anyon gas interacting through the repulsive potential of the form . All the cusps for the unpolarized spin- as well as spinless cases disappear in the limit, where is a frequency of the harmonic oscillator which is introduced as a regularization method. As g approaches zero, the result reduces to the noninteracting hard-core limit.
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/r2(g>0)g/r^2 (g > 0)g/r2(g>0). All the cusps for the unpolarized spin-1/2 as well as spinless cases disappear in the omegato0\\omega \\to 0omegato0 limit, where omega\\omegaomega is a frequency of harmonic oscillator which is introduced as a regularization method. As ggg 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/r2{\mathit{r}}^{2}r2. 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.
We study the thermodynamic properties of the anyon gas in the presence of a contact interaction. In particular, we use dimensional and analytical regularizations to calculate the second virial coefficient for free and contact-interacting anyons. The Bethe-Uhlenbeck formula is discussed and it is shown that the same result is regained using the \ensuremath{\zeta} regularization. Finally, the second virial coefficients for contact-interacting particles in two and three spatial dimensions are obtained as special cases. \textcopyright{} 1996 The American Physical Society.
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}r1{\mathbf{r}}_{1}r1​-r2{\mathbf{r}}_{2}r2​\ensuremath{\Vert}), where r2{\mathit{r}}^{2}r2U(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.