Spontaneous Symmetry Breaking at Two Loop in 3-d Massless Scalar   Electrodynamics
  In three dimensional Maxwell-Chern-Simons massless scalar electrodynamics with $ \phi^6$ coupling, the $U(1)$ symmetry is spontaneously broken at two loop order regardless of the presence or absence of the Maxwell term. Dimensional transmutation takes place in pure Chern-Simons scalar electrodynamics. The beta function for the $\phi^6$ coupling is independent of gauge couplings. 
Pang-Ning Tan, Bayram Tekin and Yutaka Hosotani (Univ of Minnesota)