Abstract
We present a systematic study of the one-loop effective potential in U(1)-invariant theories involving scalars, fermions, and gauge fields in (2+1)-dimensional space. We first consider a scale-invariant theory and find that no radiative symmetry breaking is induced. A similar result is obtained for the case of ordinary QED and Chern-Simons QED. However, radiative symmetry breaking always occurs when the scalar is also coupled to a charged fermion. We then verify that symmetry is restored at high temperature.
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