Massless Scalar QED with Non-minimal Chern Simons Coupling
  2+1 dimensional massless scalar QED with $(\phi^*\phi)^3$ scalar self-coupling is modified by the addition of a non- minimal Chern-Simons term that couples the dual of the electromagnetic field strength to the covariant current of the complex scalar field. The theory is shown to be fully one- loop renormalizable. The one loop effective potential for the scalar field gives rise to spontaneous symmetry breaking which induces masses for both the scalar and vector fields. At high temperature there is a symmetry restoring phase transition. 
M.E. Carrington and G. Kunstatter