Long-range interaction and heterogeneity yield a different kind of critical phenomenon

DNA denaturation, wetting in two dimensions, depinning of a flux line, and other problems are known to map onto a phase transition with effective long-range interaction. In a disordered system the latter yields a giant, nonuniversal, temperature-dependent critical index, and macroscopic fluctuations at a finite distance from the critical temperature. In the vicinity of the critical region the Gibbs distribution is invalid, and thermodynamics must be calculated from first principles. There are no fluctuations above the critical temperature.