Emergent power-law interactions in disordered crystals

TL;DR

This paper derives exact results for energy fluctuations caused by microscopic disorder in near-crystalline systems, revealing emergent power-law interactions between defects that reflect underlying crystal symmetry.

Contribution

It introduces a formalism to predict defect interaction energies and their fluctuations in disordered athermal systems, highlighting emergent power-law behavior and symmetry properties.

Findings

Interaction energy scales as  with defect separation

Interactions exhibit sixfold symmetry of the reference crystal

Fluctuations encode disorder-induced correlations

Abstract

We derive exact results for the fluctuations in energy produced by microscopic disorder in near-crystalline athermal systems. Our formalism captures the heterogeneity in the elastic energy of polydispersed soft disks in energy-minimized configurations. We use this to predict the distribution of interaction energy between two defects in a disordered background. We show this interaction energy displays an average power-law behaviour $\langle \delta E \rangle \sim \Delta^{-4}$ at large distances $\Delta$ between the defects. These interactions upon disorder average also display the sixfold symmetry of the underlying reference crystal. Additionally, we show that the fluctuations in the interaction energy encode the athermal correlations introduced by the disordered background. We verify our predictions with energy minimized configurations of polydispersed soft disks in two dimensions.