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

TL;DR

This paper investigates the universal properties and critical behavior of elastic manifolds in media with long-range correlated disorder, deriving renormalization-group equations and analyzing fixed points for equilibrium and depinning transitions.

Contribution

It introduces a double epsilon and delta expansion to analyze the effects of long-range correlated disorder on elastic manifolds, including fixed points and critical exponents.

Findings

Long-range disorder generates short-range disorder with a cusp in the correlator.

Critical exponents are computed to first order in epsilon and delta.

A depinning velocity-force exponent larger than one can occur.

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.