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

Andrei A. Fedorenko; Pierre Le Doussal; Kay Joerg Wiese

doi:10.1103/physreve.74.061109

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

Andrei A. Fedorenko·Pierre Le Doussal·Kay Joerg Wiese

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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 us to describe the universal properties of the system in equilibrium and at the depinning transition. Using a double epsilon=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 epsilon 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.

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Andrei A. Fedorenko, Pierre Le Doussal, Kay Joerg Wiese. 2007-01-20. Statics and dynamics of elastic manifolds in media with long-range correlated disorder. https://doi.org/10.1103/physreve.74.061109

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