Critical Fluctuations and Disorder at the Vortex Liquid to Crystal Transition in Type-II Superconductors

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 $1 4$ indicating a first order transition for n0ex0ex=0ex0ex2. We speculate that the recent experimental findings that disorder removes the first order transition are consistent with these calculations.