(4-DIMENSIONAL ELASTIC MANIFOLDS IN RANDOM-MEDIA - A RENORMALIZATION-GROUP ANALYSIS(N))

Motivated by the problem of weak collective pinning of vortex lattices in high-temperature superconductors, we study the model system of a f our-dimensional elastic manifold with N transverse degrees of freedom (4 + N model) in a quenched disorder environment. We assume the disord er to be weak and short-range correlated, and neglect thermal effects. Using a real-space functional renormalization-group (FRG) approach, w e derive a RG equation for the pinning-energy correlator up to a two-l oop correction. The solution of this equation allows us to calculate t he size R-c of collectively pinned elastic domains as well as the crit ical force F-c, i.e., the smallest external force needed to drive thes e domains. We find R-c proportional to delta(alpha 2) exp(alpha(1)/del ta(p)) and F-c proportional to delta(p)(-2 alpha 2) exp(-2 alpha(1)/de lta(p)), where delta(p) much less than 1 parametrizes the disorder str ength alpha(1) = (2/pi)(N/2)8 pi(2)/(N + 8), and alpha(2) = 2(5N + 22) /(N + 8)(2). In contrast to lowest-order perturbation calculations whi ch we briefly review, we thus arrive at determining both alpha(1) (one loop) and alpha(2) (two loop).