Destruction of the phase coherence by the magnetic field in the   fluctuation region of thin superconducting film
  It was shown as long ago as 1998 cond-mat/9811051 that the vortex lattice melting theories are science fiction because the Abrikosov state is not the vortex lattice with crystalline long-range order. Nevertheless this false conception is used up to now in many works including the lecture notes cond-mat/0111052 providing a pedagogical introduction. This false conception has resulted from visual but incorrect ideas. In spite of outward appearances only long-range order - long-range phase coherence exists in the Abrikosov state. The phase transition interpreted erroneously as the vortex lattice melting is in reality a disappearance of long-range phase coherence. The investigation of the nonlocal resistivity made in this work is experimental evidence that a state without phase coherence, differed qualitatively from mythical vortex liquid, is observed above this transition. 
A.V. Nikulov, S.V. Dubonos and Y.I. Koval