Topological Defects in the Random-Field XY Model and the Pinned Vortex Lattice to Vortex Glass Transition in Type-II Superconductors

TL;DR

This study uses Monte Carlo simulations to explore topological defect behavior in the random-field XY model, suggesting a phase transition in three dimensions that relates to vortex lattice transitions in type-II superconductors.

Contribution

It provides evidence for a topological phase transition at nonzero field in the 3D random-field XY model, linking it to vortex glass transitions in superconductors.

Findings

Vortex spacing diverges more strongly than Imry-Ma length as field decreases.

Evidence for a nonzero critical field $H_c$ for a defect-free phase in 3D.

Connection established between the phase transition and vortex glass formation.

Abstract

As a simplified model of randomly pinned vortex lattices or charge-density waves, we study the random-field XY model on square ($d=2$) and simple cubic ($d=3$) lattices. We verify in Monte Carlo simulations, that the average spacing between topological defects (vortices) diverges more strongly than the Imry-Ma pinning length as the random field strength, $H$, is reduced. We suggest that for $d=3$ the simulation data are consistent with a topological phase transition at a nonzero critical field, $H_c$, to a pinned phase that is defect-free at large length-scales. We also discuss the connection between the possible existence of this phase transition in the random-field XY model and the magnetic field driven transition from pinned vortex lattice to vortex glass in weakly disordered type-II superconductors.