Non-Universal Quasi-Long Range Order in the Glassy Phase of Impure Superconductors

The structural correlation functions of a weakly disordered Abrikosov lattice are calculated for the first time in a systematic RG-expansion in d=4-\epsilon dimensions. It is shown, that in the asymptotic limit the Abrikosov lattice exhibits still quasi long range translational order described by a non-universal exponent \bar\eta_{\bf G} which depends on the ratio of the renormalized elastic constants \kappa =\tilde c_{66}/\tilde c_{11} of the flux line (FL) lattice. Our calculations show clearly three distinct scaling regimes corresponding to the Larkin, the manifold and the asymptotic Bragg glass regime. On a wide range of intermediate length scales the FL displacement correlation function increases as a power law with twice of the manifold roughness exponent \zeta_{rm}(\kappa), which is also non-universal. Our results, in particular the \kappa-dependence of the exponents, are in variance with those of the variational treatment with replica symmetry breaking which allows in principle an experimental discrimination between the two approaches.