The effect of weak impurity disorder on flux lattices at equilibrium is studied in the absence of free dislocations using both the Gaussian variational method and, to O(ε=4-d), the functional renormalization group. We find universal logarithmic growth of displacements for 2<d<4:〈u(x)-u(0)${\mathrm{〉}}^2$¯∼${\mathit{A}}_{\mathit{d}}$ln‖x‖ and persistence of algebraic quasi-long-range translational order. When the two methods can be compared they agree within 10% on the value of ${\mathit{A}}_{\mathit{d}}$. We compute the function describing the crossover between the ‘‘random manifold’’ regime and the logarithmic regime. A similar crossover could be observable in present decoration experiments.

• Received 16 March 1993

DOI:https://doi.org/10.1103/PhysRevLett.72.1530