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Phase transition in U(n)xU(n) models is investigated for arbitrary flavornumber n. We present a nonperturbative, 3+1 dimensional finite temperaturetreatment of obtaining the effective potential, based on a chiral invariantexpansion of the functional renormalization group flows. The obtained tower ofequations is similar but not identical to that of the Dyson-Schwinger hierarchyand has to be truncated for practical purposes. We investigate the finitetemperature behavior of the system in an expansive set of the parameter spacefor n = 2, 3, 4 and also perform a large-n analysis. Our method is capable ofrecovering the one-loop beta functions of the coupling constants of the epsilonexpansion; furthermore, it shows direct evidence that regardless of the actualflavor number, within our approximation, the system undergoes a fluctuationinduced first order phase transition.

Fluctuation induced first order phase transition in U(n)xU(n) models using chiral invariant expansion of functional renormalization group flows