Chaos and residual correlations in pinned disordered systems

Abstract

We study, using functional renormalization (FRG), two copies of an elastic system pinned by mutually correlated random potentials. Short scale decorrelation depend on a non trivial boundary layer regime with (possibly multiple) chaos exponents. Large scale mutual displacement correlation behave as $|x-x^{\prime }{|}^{2\zeta -\mu }$, the decorrelation exponent $\mu$ proportional to the difference between Flory (or mean field) and exact roughness exponent $\zeta$. For short range disorder $\mu >0$ but small, e.g. for random bond interfaces $\mu =5\zeta -\epsilon$, $\epsilon =4-d$, and $\mu =\epsilon (\frac{(2\pi {)}^2}{36}-1)$ for the one component Bragg glass. Random field (i.e long range) disorder exhibits finite residual correlations (no chaos $\mu =0$) described by new FRG fixed points. Temperature and dynamic chaos (depinning) are discussed.

5 pages

References in corpus (8)

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• Depinning of elastic manifolds
• Functional Renormalization Group and the Field Theory of Disordered Elastic Systems
• Chaos in temperature in the Sherrington-Kirkpatrick model
• Ground states and thermal states of the random field Ising model
• Can non-linear elasticity explain contact-line roughness at depinning?
• Temperature and Disorder Chaos in Low Dimensional Directed Paths
• Thermal fluctuations in pinned elastic systems: field theory of rare events and droplets

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