Absence of Two-Dimensional Bragg Glasses

TL;DR

This paper investigates the stability of the two-dimensional Bragg glass phase in disordered elastic media and finds it to be unstable to dislocations, challenging previous assumptions about its robustness.

Contribution

It provides the first numerical evidence that the two-dimensional Bragg glass is unstable to dislocations, using a minimum-cost-flow algorithm on a disordered loop model.

Findings

Two-dimensional Bragg glass is unstable to dislocations.

Dislocations energetics align with renormalization group predictions.

The elastic phase cannot sustain topological defects in 2D.

Abstract

The stability to dislocations of the elastic phase, or ``Bragg glass'', of a randomly pinned elastic medium in two dimensions is studied using the minimum-cost-flow algorithm for a disordered fully-packed loop model. The elastic phase is found to be unstable to dislocations due to the quenched disorder. The energetics of dislocations are discussed within the framework of renormalization group predictions as well as in terms of a domain wall picture.