  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,
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 $\alpha$ and $\nu$ that vary continuously with the strength of the CS
term, and a comparison with available analytical results is made.
