QED in 2+1 dimensions, analyzed in the 1/N expansion, is shown to exhibit a critical behavior as the number N of fermions approaches 32π². The dynamical mass has a universal scaling behavior at the critical point. The existence of criticality is discovered first by an analytic study of the gap equation and the effective potential. Its existence and universality is then confirmed numerically. Similarities to four-dimensional theories are discussed.
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Appelquist et al. (1988) studied this question.
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