Application of Polynomial Algorithms to a Random Elastic Medium

TL;DR

This paper investigates the stability of a two-dimensional disordered elastic medium, demonstrating through polynomial algorithms that dislocations unbind at large scales, indicating the absence of a Bragg glass phase in such systems.

Contribution

It applies polynomial algorithms to analyze dislocation energetics in a disordered elastic medium, providing new insights into phase stability.

Findings

Dislocations unbind at large scales in 2D

Elastic phase is unstable in the presence of disorder

No Bragg glass phase exists in the studied model

Abstract

A randomly pinned elastic medium in two dimensions is modeled by a disordered fully-packed loop model. The energetics of disorder-induced dislocations is studied using exact and polynomial algorithms from combinatorial optimization. Dislocations are found to become unbound at large scale, and the elastic phase is thus unstable giving evidence for the absence of a Bragg glass in two dimensions.