Phase Transitions and Mass Generation in 2+1 Dimensions

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 $N$ 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.