Long range interaction yields a new kind of phase transition

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DNA denaturation, wetting in two dimensions, depinning of a flux line, and other problems map onto a phase transition with effective long range interaction. It yields giant non-universal critical indexes, arbitrarily large macroscopic correlation length and fluctuations at a finite distance from the critical temperature. In the vicinity of this region the Gibbs distribution is invalid, and thermodynamics must be calculated from the first principles. There are no fluctuations above the critical temperature.