Effect of wave function renormalization in N-flavor three-dimensional QED at finite temperature.

A recent study of dynamical chiral symmetry breaking in N flavor three-dimensional QED at finite temperature is extended to include the effect of fermion wave function renormalization in the Schwinger-Dyson equations. The simple ``zero-frequency'' truncation previously used is found to lead to unphysical results, especially as T\ensuremath{\rightarrow}0. A modified set of equations is proposed, whose solutions behave in a way which is qualitatively similar to the T=0 solutions of Pennington and co-workers who have made extensive studies of the effect of wave function renormalization in this context, and who concluded that there was no critical ${\mathit{N}}_{\mathit{c}}$ (at T=0) above which chiral symmetry was restored. In contrast, we find that our modified equations predict a critical ${\mathit{N}}_{\mathit{c}}$ at T\ensuremath{\ne}0, and an N-T phase diagram very similar to the earlier study neglecting wave function renormalization. The reason for the difference is traced to the different infrared behavior of the vacuum polarization at T=0 and at T\ensuremath{\ne}0.