2+1 Dimensional QED and a Novel Phase Transition

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Abstract
We investigate the chiral phase transition in 2+1 dimensional QED. Previous gap equation and lattice Monte-Carlo studies of symmetry breaking have found that symmetry breaking ceases to occur when the number of fermion flavors exceeds a critical value. Here we focus on the order of the transition. We find that there are no light scalar degrees of freedom present as the critical number of flavors is approached from above (in the symmetric phase). Thus the phase transition is not second order, rendering irrelevant the renormalization group arguments for a fluctuation induced transition. However, the order parameter vanishes continuously in the broken phase, so this transition is also unlike a conventional first order phase transition.