The vortex lattice melting theory as example of science fiction

The concept of the transition of type II superconductor into the Abrikosov state as the appearance of long-range phase coherence is considered. It is shown that this transition should be first order in ideal (without disorder) superconductor. Such transition is indeed observed in bulk superconductors with weak disorder at a field Hc4 < Hc2. No experimental evidence of the vortex lattice melting exists now. It is shown that this popular concept has appeared on a consequence of an incorrect interpretation of the Abrikosov state and incorrect definition of the phase coherence. The absence of a sharp transition in thin films with weak disorder is interpreted as absence of long-range phase coherence down to very low magnetic field. In order to explain the observed smooth phase coherence appearance in superconductors with strong disorder it is proposed to return to the Mendelssohn model.