VARIATIONAL THEORY FOR THE PINNING OF VORTEX LATTICES BY IMPURITIES

We derive a variational replica-symmetry-breaking theory for the effect of random impurities on equilibrium properties of general ordered (crystalline) structures, in particular two-and three-dimensional vortex lattices and magnetic bubble films. We investigate the role of a finite correlation length for the random potential and show that the short scale behavior of the correlation functions corresponds to the results of Larkin and Ovchinnikov. For larger scales, we find that the translational correlation functions decay as stretched exponentials with exponents, which take different values: one must distinguish between a regime where the typical displacement is much smaller than the lattice spacing and a regime where it is much larger. We predict that, in the absence of dislocations, long-range orientational order is maintained in three and two dimensions. Our results appear to be in agreement with existing experimental data.