Abstract
The possibility that the epsilon expansion can predict the order of phase transitions in three dimensional field theories is examined. For a Hermitean matrix-valued order parameter, the epsilon expansion predicts fluctuation induced first order phase transitions. We analyze two 2+1-dimensional quantum field theories which exhibit spontaneous symmetry breaking and have martix order parameters. Using the large expansion, we show that these models exhibit second order transitions and discuss the implications for the chiral symmetry breaking transition in 2+1-dimensional QCD for a critical number of quark flavors.
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