Vortex-liquid-vortex-crystal transition in type-II superconductors

We present in detail a functional renormalization group (FRG) study of a Landau-Ginzburg model of type-II superconductors (generalized to N/2 complex fields) in an external magnetic field, both for a pure system and also in the presence of quenched random impurities. If the coupling functions are restricted to the space of functions with nonzero support only at reciprocal lattice vectors corresponding to the Abrikosov lattice, we find a stable FRG fixed point in the presence of disorder for 1 4. The nonzero-temperature transition will disappear in physical dimensions. The pure system has a stable fixed point only for N>4. Therefore the physical case (N=2) is likely to have a first-order transition in the absence of quenched disorder. We give a full discussion of both the motivation of the model and the details of the FRG calculation. We also place our results in context with regard to the current experimental scene concerning the high-T compounds. In particular, we discuss the relevance of our results to the recently discovered critical end point in the phase diagram of Bi-Sr-Ca-Cu-O. The main results of this analysis were previously reported in the form of a Letter [M.A. Moore and T.J. Newman, Phys. Rev. Lett. 75, 533 (1995)].