Phase transition of N-component superconductors

We investigate the phase transition in the three-dimensional Abelian Higgs model for N complex scalar fields, using the gauge-invariant average action Gamma(k). The dependence of Gamma(k) on the effective infrared cutoff k is described by a nonperturbative flow equation. The transition turns out to be first or second order, depending on the ratio between the scalar and gauge coupling. We look at the fixed points of the theory for various N and compute the critical exponents of the model. Our results suggest the existence of a parameter range with a second order transition for all N, including the case of the superconductor phase transition for N = 1.