Topological Defects in the Random-Field XY Model and Randomly Pinned Vortex Lattices

TL;DR

This paper investigates the behavior of topological defects in the random-field XY model, revealing a divergence in vortex spacing and evidence of a phase transition to a vortex-free phase in three dimensions.

Contribution

It provides new simulation evidence on vortex behavior and phase transitions in the random-field XY model across different dimensions.

Findings

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

Evidence of a topological phase transition at nonzero field in 3D

Simulation results support theoretical predictions about vortex behavior

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 argue, and confirm in simulations, that the spacing between topological defects (vortices) diverges more strongly than the Imry-Ma pinning length as the random field strength, $H$, is reduced. For $d=3$ the data are consistent with a topological phase transition at a nonzero $H_c$ to a vortex-free pinned phase.