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

Andrei A. Fedorenko, Pierre Le Doussal, Kay Jörg Wiese
CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75005 Paris, France

Abstract

We study the statics and dynamics of an elastic manifold in a disordered medium with quenched defects correlated as ~ r^{- a} for large separation r. We derive the functional renormalization group equations to one-loop order which allow to describe the universal properties of the system in equilibrium and at the depinning transition. Using a double ε=4-d and δ=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 ε and δ at the fixed points. At depinning a velocity-versus-force exponent β larger than unity can occur. We discuss possible realizations using extended defects.

cond-mat/0607229 [pdf]
Phys. Rev. E 74 (2006) 061109 [pdf]