Statics and dynamics of elastic manifolds in media with long-range correlated disorder

We study the statics and dynamics of an elastic manifold in a disordered medium with quenched defects correlated as $\sim r^{-a} $ for large separation $r$. We derive the functional renormalization group equations to one-loop order, which allow us to describe the universal properties of the system in equilibrium and at the depinning transition. Using a double $\varepsilon=4-d$ and $\delta=4-a$ expansion, we compute the fixed points characterizing different universality classes and analyze their regions of stability. The long-range disorder-correlator remains analytic but generates short-range disorder whose correlator exhibits the usual cusp. The critical exponents and universal amplitudes are computed to first order in $\varepsilon$ and $\delta$ at the fixed points. At depinning, a velocity-versus-force exponent $\beta$ larger than unity can occur. We discuss possible realizations using extended defects.