Abstract
It is shown that phase fluctuations destroy off-diagonal long-range order (phase coherence) in the Meissner phase below two dimensions, below four dimensions in the conventional Abrikosov flux-lattice phase, and below three dimensions in the limit of infinite Ginzburg ratio \ensuremath{\kappa}. The destruction of long-range order in the flux lattice is due to phase changes induced by shear motions of the flux lines. The phase coherence decays over a long length scale (of order millimeters) in three-dimensional systems.
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