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We study elastic systems such as interfaces or lattices pinned by correlatedquenched disorder considering two different types of correlations: generalizedcolumnar disorder and quenched defects correlated as ~ x^{-a} for largeseparation x. Using functional renormalization group methods, we obtain thecritical exponents to two-loop order and calculate the response to a transversefield h. The correlated disorder violates the statistical tilt symmetryresulting in nonlinear response to a tilt. Elastic systems with columnardisorder exhibit a transverse Meissner effect: disorder generates the criticalfield h_c below which there is no response to a tilt and above which the tiltangle behaves as \theta ~ (h-h_c)^{\phi} with a universal exponent \phi<1. Thisdescribes the destruction of a weak Bose glass in type-II superconductors withcolumnar disorder caused by tilt of the magnetic field. For isotropiclong-range correlated disorder, the linear tilt modulus vanishes at smallfields leading to a power-law response \theta ~ h^{\phi} with \phi>1. Theobtained results are applied to the Kardar-Parisi-Zhang equation withtemporally correlated noise.

Elastic systems with correlated disorder: Response to tilt and application to surface growth