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

TL;DR

This study explores how adding a Chern-Simons term to the three-dimensional XY model affects vortex properties and critical behavior, revealing that the model remains in the XY universality class with a critical temperature that increases with internal angular momentum.

Contribution

It introduces the Chern-Simons term into the 3D XY model and investigates its effects using Monte Carlo simulations, highlighting changes in vortex properties and critical temperature.

Findings

Model belongs to XY universality class

Critical temperature increases with internal angular momentum

Vortices acquire internal angular momentum and arbitrary statistics

Abstract

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.