Phase structure of Abelian Chern-Simons gauge theories

We study the effect of a Chern-Simons (CS) term in the phase structure of two different Abelian gauge theories. For the compact Maxwell-Chern-Simons theory, with the CS term properly defined, we obtain that for values $g=n/2\pi$ of the CS coupling with $n=\pm 1$, $\pm 2$, the theory is equivalent to a gas of closed loops with contact interaction, exhibiting a phase transition in the $3dXY$ universality class. We also employ Monte Carlo simulations to study the noncompact $U(1)$ Abelian Higgs model with a CS term. Finite-size scaling of the third moment of the action yields critical exponents α and ν that vary continuously with the strength of the CS term, and a comparison with available analytical results is made.