We present a functional renormalization group (FRG) analysis of a Landau-Ginzburg model of type-II superconductors (generalized to n/2 complex fields) in a magnetic field, for both a pure and a disordered system. The disordered system supports a stable FRG fixed point for 1 <n <4, identical to that of the disordered O(n) model in d - 2 dimensions. The pure system has a stable fixed point only for n > 4 indicating a first order transition for n = 2. We speculate that the recent experimental findings that disorder removes the first order transition are consistent with these calculations.
Moore, M. A., & Newman, T. J. (1995). Critical fluctuations and disorder at the vortex liquid to crystal transition in type-II superconductors. Physical Review Letters, 75(3), 533-536. https://doi.org/10.1103/PhysRevLett.75.533