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

Abstract

We study elastic systems such as interfaces or lattices pinned by correlated quenched disorder considering two different types of correlations: generalized columnar disorder and quenched defects correlated as $\ensuremath{\sim}{x}^{\ensuremath{-}a}$ for large separation $x$. Using functional renormalization group methods, we obtain the critical exponents to two-loop order and calculate the response to a transverse field $h$. The correlated disorder violates the statistical tilt symmetry resulting in nonlinear response to a tilt. Elastic systems with columnar disorder exhibit a transverse Meissner effect: disorder generates the critical field ${h}_{c}$ below which there is no response to a tilt and above which the tilt angle behaves as $\ensuremath{\vartheta}\ensuremath{\sim}{(h\ensuremath{-}{h}_{c})}^{\ensuremath{\phi}}$ with a universal exponent $\ensuremath{\phi}l1$. This describes the destruction of a weak Bose glass in type-II superconductors with columnar disorder caused by tilt of the magnetic field. For isotropic long-range correlated disorder, the linear tilt modulus vanishes at small fields leading to a power-law response $\ensuremath{\vartheta}\ensuremath{\sim}{h}^{\ensuremath{\phi}}$ with $\ensuremath{\phi}g1$. The obtained results are applied to the Kardar-Parisi-Zhang equation with temporally correlated noise.