Why Vortex Lattice Melting Theory is Science Fiction

The distinguished work by A.A. Abrikosov awarded of the Nobel Prize in Physics for 2003 not only has determined the orientation of all investigations of the mixed state of type II superconductors during forty years but also has provoked a mass delusion. Most scientists consider the Abrikosov state first of all as a vortex lattice. But Abrikosov has found a periodic lattice structure with crystalline long-rang order only because that he searched it. It is impossible to obtain any other result besides a periodical structure for the case of homogeneous, symmetric, infinite space. The long-rang order of superconducting state is phase coherence. It is strange that most scientists have lightly admitted that the Abrikosov state can have two long-rang order although only phase transition is assumed always on the way from this state in the normal state. Moreover, the vortex lattice is considered by many scientists as only long-rang order of the Abrikosov state and therefore vortex lattice melting is one of the most popular themes in physics of superconductors during last 15 years. 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 can not be interpreted as vortex lattice melting. History of the problem is considered 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. 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.