Three-dimensional $x-y$ model with the Chern-Simons term

Details Three-dimensional $x-y$ model with the Chern-Simons term Three-dimensional $x-y$ model with the Chern-Simons term

1994-11-16

arxiv.org/abs/hep-lat/9411026v1

Physics

High Energy Physics

High Energy Physics - Lattice

15 pages, uuencoded postscript file

Scientific paper

We investigate the influence of the Chern-Simons term coupled to the three-dimensional $x-y$ model. This term endows vortices with an internal angular momentum and thus gives them arbitrary statistics. The Chern-Simons term for the $x-y$ model takes an integer value which can be written as a sum over all vortex lines of the product of the vortex charge and the winding number of the internal phase angle along that vortex line. We have used the Monte-Carlo method to study the three-dimensional $x-y$ model with the Chern-Simons term. Our findings suggest that this model belongs to the $x-y$ universality class with the critical temperature growing with increasing internal angular momentum.

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