Response of manifolds pinned by quenched impurities to uniform and random perturbations

The singular response in the thermodynamic and geometric properties of manifolds pinned by quenched disorder to local and global perturbations is considered. The averaged displacement of a linear-extent L manifold is proportional to ${\mathit{pL}}_{\mathit{p}}^{\mathrm{\zeta }+\mathrm{\phi }}$, where p is the (small p<${\mathit{L}}_{\mathit{p}}^{\mathrm{-}1/\mathrm{\phi }}$) magnitude of the perturbation, ζ is the unperturbed roughness exponent, and ${\mathrm{\phi }}_{\mathit{p}}$ is a crossover exponent which is calculated for a variety of uniform and random perturbations. Applications to random magnets, polymers, flux lines, and magnetoresistance of localized electrons are discussed.