Phase diagram of superconductors from nonperturbative flow equations

The universal behavior of superconductors near the phase transition is described by the three-dimensional field theory of scalar quantum electrodynamics. We approximately solve the model with the help of nonperturbative flow equations. A first- or second-order phase transition is found depending on the relative strength of the scalar versus the gauge coupling. The region of a second-order phase transition is governed by a fixed point of the flow equations with associated critical exponents. We also give an approximate description of the tricritical behavior and briefly discuss the crossover relevant for the onset of scaling near the critical temperature. Final confirmation of a second-order transition for strong type-II superconductors requires further analysis with extended truncations of the flow equations.