Nonuniversal Correlations and Crossover Effects in the Bragg-Glass Phase of Impure Superconductors

Abstract

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.