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We study the vortex-line lattice and liquid phases of a clean type-IIsuperconductor by means of Monte Carlo simulations of the lattice London model.Motivated by a recent controversy regarding the presence, within this model, ofa vortex-liquid regime with longitudinal superconducting coherence over longlength scales, we directly compare two different ways to calculate thelongitudinal coherence. For an isotropic superconductor, we interpret ourresults in terms of a temperature regime within the liquid phase in whichlongitudinal superconducting coherence extends over length scales larger thanthe system thickness studied. We note that this regime disappears in themoderately anisotropic case due to a proliferation, close to the flux-linelattice melting temperature, of vortex loops between the layers.Comment: 8 pages, Revtex, with eps figures. To appear in Phys. Rev.

Vortex-line liquid phases: Longitudinal superconductivity in the lattice London model