  The structural correlation functions of a weakly disordered Abrikosov lattice
are calculated in a functional 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 {\it nonuniversal} exponent
$\eta_{\bf G}$ which depends on the ratio of the renormalized elastic constants
$\kappa ={c}_{66}/ {c}_{11}$ of the flux line (FL) lattice. Our calculations
clearly demonstrate three distinct scaling regimes corresponding to the Larkin,
the random manifold and the asymptotic Bragg-glass regime. On a wide range of
{\it intermediate} length scales the FL displacement correlation function
increases as a power law with twice the manifold roughness exponent $\zeta_{\rm
RM}(\kappa) $, which is also {\it nonuniversal}. Correlation functions in the
asymptotic regime are calculated in their full anisotropic dependencies and
various order parameters are examined. Our results, in particular the
$\kappa$-dependency 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.
