Dislocations in the ground state of the solid-on-solid model on a disordered substrate

TL;DR

This study explores how dislocations affect the ground state of the solid-on-solid model on a disordered substrate, revealing their role in destabilizing the elastic phase and exhibiting complex scaling behaviors.

Contribution

It provides a detailed analysis of dislocation effects on the SOS model's ground state using combinatorial optimization, highlighting their impact on phase stability and defect scaling.

Findings

Dislocations destabilize the elastic phase.

Dislocation density decreases exponentially with vortex core energy.

Maximum mean dislocation distance depends on system size and energy.

Abstract

We investigate the effects of topological defects (dislocations) to the ground state of the solid-on-solid (SOS) model on a simple cubic disordered substrate utilizing the min-cost-flow algorithm from combinatorial optimization. The dislocations are found to destabilize and destroy the elastic phase, particularly when the defects are placed only in partially optimized positions. For multi defect pairs their density decreases exponentially with the vortex core energy. Their mean distance has a maximum depending on the vortex core energy and system size, which gives a fractal dimension of $1.27 \pm 0.02$. The maximal mean distances correspond to special vortex core energies for which the scaling behavior of the density of dislocations change from a pure exponential decay to a stretched one. Furthermore, an extra introduced vortex pair is screened due to the disorder-induced defects and its energy is linear in the vortex core energy.