Disorder-Induced Topological Defects in a d=2 Elastic Medium at Zero Temperature

TL;DR

This study numerically investigates how quenched disorder influences the density and correlations of topological defects in a two-dimensional elastic medium at zero temperature, revealing exponential defect density decay and fractal defect structures.

Contribution

It introduces a detailed numerical analysis of defect densities and correlations in a disordered 2D elastic medium, highlighting the role of string-like excitations and defect screening effects.

Findings

Defect density decreases exponentially with core energy.

String-like excitations have a fractal dimension of approximately 1.25.

Disorder-induced defects screen vortex pair interactions at zero temperature.

Abstract

The density and correlations of topological defects are investigated numerically in a model of a d=2 elastic medium subject to a periodic quenched random potential. The computed density of defects decreases approximately exponentially with the defect core energy. Comparing the defect-free ground state with the ground state with defects, it is found that the difference is described by string-like excitations, bounded by defect pairs, which have a fractal dimension of 1.250(3). At zero temperature, the disorder-induced defects screen the interaction of introduced vortex pairs.