  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.
