  Five years ago the talk "The vortex lattice melting theory as example of
science fiction" cond-mat/9811051 was presented. Nevertheless this theory
predominates up to now and very many people devote oneself to it. It is
explained in the present paper why the only first order phase transition
observed on the way from the Abrikosov state in the normal state should be
interpreted as phase coherence disappearance. The false concept of vortex
lattice melting appeared because of some causes main of them are erroneous
interpretation of direct observation of the Abrikosov state and the use by
theorists the habitual determination of phase coherence invalid for
multi-connected superconducting state. The distinguished work by A.A. Abrikosov
awarded of the Nobel Prize in Physics for 2003 predicted a periodic lattice
structure with crystalline long-rang order only because that it is impossible
to obtain any other result for the case of homogeneous, symmetric, infinite
space. It is strange that most scientists have lightly admitted that this
prediction corresponds to the facts. The long-rang order of superconducting
state is phase coherence. Therefore if the Abrikosov state is also the vortex
lattice then it have two long-rang orders and two phase transition may be
expected. But only phase transition is assumed and observed always. History of
this contradiction is considered in the present paper and it is analysed why
some delusions about the Abrikosov state became popular. It is emphasized that
taking into account thermal fluctuations changes in essence the habitual notion
about the mixed state of type II superconductor built because of the Abrikosov
result. First of all it shows that the Abrikosov solution is not valid just in
the ideal case for which it was obtained.
