Nonuniversal correlations and crossover effects in the Bragg-glass phase of impure superconductors

The structural correlation functions of a weakly disordered Abrikosov lattice are calculated in a functional RG expansion in $d=4\mathrm{}-\epsilon$ dimensions. It is shown that in the asymptotic limit the Abrikosov lattice exhibits still quasi-long-range translational order described by a nonuniversal exponent ${\eta }_{\mathbf{G}}$ 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 intermediate length scales the FL displacement correlation function increases as a power law with twice the manifold roughness exponent ${\zeta }_{\mathrm{RM}}\left(\kappa \right),$ which is also 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.