Localization of Elastic Layers by Correlated Disorder

TL;DR

This paper investigates the behavior of elastic layers with correlated disorder using renormalization group methods, revealing a localized glassy phase with specific displacement characteristics and stability properties.

Contribution

It introduces a theoretical analysis of elastic layers with correlated disorder, identifying a stable localized glassy phase and its properties across dimensions.

Findings

Displacements grow logarithmically transverse to correlation direction.

Displacements are strongly localized along the correlation direction.

The localized phase remains stable against point disorder.

Abstract

The equilibrium behavior of a system of elastic layers under tension in the presence of correlated disorder is studied using functional renormalization group techniques. The model exhibits many of the features of the Bose glass phase of type II superconductors induced by columnar defects, but may be more directly applicable to charge density waves, incommensurate striped magnetic phases, stacked membranes under tension, vicinal crystal surfaces, or superconducting ``vortex--chains''. Below five dimensions, an epsilon expansion for the stable zero temperature fixed point yields the properties of the glassy phase. Transverse to the direction of correlation, the randomness induces logarithmic growth of displacements. Displacements are strongly localized in the correlation direction. The absence of a response to a weak applied transverse field (transverse Meissner effect) is demonstrated analytically. In this simple model, the localized phase is stable to point disorder, in contrast to the behavior in the presence of dislocations, in which the converse is believed to be true.