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, Hc, 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. PACS: 05.70.Jk, 64.60.Fr, 64.70.Pf, 75.50.Lk Typeset using REVTEX