We carry out simulations of a lattice London superconductor in a magnetic field B, with a finite magnetic penetration length λ. We find that superconducting coherence parallel to B persists into the vortex line liquid. We argue that the length scale relevant to this effect is Λ = φ0/8πTm. 74.60.Ge, 64.60-i, 74.40.+k Typeset using REVTEX
