  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.
