ELASTIC THEORY OF PINNED FLUX LATTICES

The effect of weak impurity disorder on flux lattices at equilibrium i s studied in the absence of free dislocations using both the Gaussian variational method and, to O(epsilon = 4 - d), the functional renormal ization group. We find universal logarithmic growth of displacements f or 2 < d < 4: [u(x) - u(0)]2BAR is similar to A(d) ln Absolute value o f x and persistence of algebraic quasi-long-range translational order. When the two methods can be compared they agree within 10% on the val ue of A(d). We compute the function describing the crossover between t he ''random manifold'' regime and the logarithmic regime. A similar cr ossover could be observable in present decoration experiments.