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

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.

6 pages RevTeX, eps figures included

References in corpus (5)

• Stability of Elastic Glass Phases in Random Field XY Magnets and Vortex Lattices in Type II Superconductors
• Absence of Two-Dimensional Bragg Glasses
• Ground-State Roughness of the Disordered Substrate and Flux Line in d=2
• Ground state properties of fluxlines in a disordered environment
• Application of Polynomial Algorithms to a Random Elastic Medium

Cited by in corpus (5)

• Domain walls and chaos in the disordered SOS model
• Critical properties of loop percolation models with optimization constraints
• Disorder Driven Critical Behavior of Periodic Elastic Media in a Crystal Potential
• Roughening and superroughening in the ordered and random two-dimensional sine-Gordon models
• A periodic elastic medium in which periodicity is relevant