Topological defects in the random-field XY model and the pinned vortex lattice to vortex glass transition in type-II superconductors

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 (Formula presented) 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 a pinned vortex lattice to a vortex glass in weakly disordered type-II superconductors.