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

Phase transition in U(n)xU(n) models is investigated for arbitrary flavor number n. We present a nonperturbative, 3+1 dimensional finite temperature treatment of obtaining the effective potential, based on a chiral invariant expansion of the functional renormalization group flows. The obtained tower of equations is similar but not identical to that of the Dyson-Schwinger hierarchy and has to be truncated for practical purposes. We investigate the finite temperature behavior of the system in an expansive set of the parameter space for n = 2, 3, 4 and also perform a large-n analysis. Our method is capable of recovering the one-loop beta functions of the coupling constants of the epsilon expansion; furthermore, it shows direct evidence that regardless of the actual flavor number, within our approximation, the system undergoes a fluctuation induced first order phase transition.