Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2006-09-10
Phys. Rev. E 74, 061109 (2006)
Physics
Condensed Matter
Disordered Systems and Neural Networks
16 pages, 11 figures, revtex4
Scientific paper
10.1103/PhysRevE.74.061109
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.
Doussal Pierre Le
Fedorenko Andrei A.
Wiese Kay Joerg
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