Is there a phase transition in Maxwell-Chern-Simons theory?

Abstract

We reexamine recent work on the Abelian Higgs model (scalar QED) in 2 + 1 dimensions. We compute the effective potential at finite temperature using the Vilkovisky-DeWitt formalism and show that there is spontaneous symmetry breaking at one loop. We use an effective action formalism to take into account ring corrections and find that classically broken symmetries can be restored at high temperature. The presence of the Chern-Simons parameter can hinder symmetry breaking for values of the self-couplings very close to the critical value normally required for a phase transition