Chaos and residual correlations in pinned disordered systems

TL;DR

This paper uses functional renormalization to analyze correlations and chaos in two coupled disordered elastic systems, revealing how disorder type and scale influence residual correlations and chaos exponents.

Contribution

It introduces a detailed FRG analysis of mutual correlations and chaos exponents in pinned disordered systems, including new fixed points for long-range disorder.

Findings

Mutual displacement correlations scale as |x-x'|^{2ζ - μ}

Residual correlations exist for long-range disorder with μ=0

Short-range disorder shows small chaos exponents μ > 0

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 $|x-x'|^{2 \zeta - \mu}$, 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.