Abstract
We study, using functional renormalization, two copies of an elastic system pinned by mutually correlated random potentials. Short scale decorrelation depends on a nontrivial boundary layer regime with (possibly multiple) chaos exponents. Large scale mutual displacement correlations behave as [x - x'](2zeta-mu), mu proportional to the difference between Flory (or mean field) and exact roughness exponents zeta. For short range disorder mu>0 and small; e.g., for random bond interfaces mu=5zeta-epsilon, epsilon=4-d, and mu=epsilon{[(2pi)(2)/36]-1} for the one component Bragg glass. Random field (i.e., long range) disorder exhibits finite residual correlations (no chaos mu=0) described by new functional renormalization fixed points. Temperature and dynamic chaos (depinning) are discussed.
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