A note on the phase transition in a topologically massive Ginzburg-Landau theory

We consider the phase transition in a model which consists of a Ginzburg-Landau free energy for superconductors including a Chern-Simons term. The mean field theory of Halperin, Lubensky and Ma [Phys. Rev. Lett. 32, 292 (1974)] is applied for this model. It is found that the topological mass, $\theta$, drives the system into different regimes of phase transition. For instance, there is a $\theta_{c}$ such that for $\theta<\theta_{c}$ a fluctuation induced first order phase transition occurs. On the other hand, for $\theta>\theta_{c}$ only the second order phase transition exists. The 1-loop renormalization group analysis gives further insight to this picture. The fixed point structure exhibits tricritical and second order fixed points.