PHASE-TRANSITIONS AND MASS GENERATION IN 2+1 DIMENSIONS

The possibility that the f expansion can predict the order of phase transitions in three-dimensional field theories is examined. For a Hermitian 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 matrix 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.