Ordered continuously degenerate systems are shown to have some common properties associated with strong transverse fluctuations of the order parameter. Longitudinal fluctuations are related to the transverse ones in three-dimensional systems. The longitudinal susceptibility is infinitely large at zero external field and the longitudinal scattering is rather strong at low wavevectors. Properties of two-dimensional degenerate systems depend on the dimensionality n of the order parameter. There is a phase transition at finite temperature T 0 for n=2. At temperatures below T 0 a ‘super-fluid density’ or ‘transverse rigidity’ arises. Probably no phase transition takes place for n≥3 since the effective temperature increases with the scale of fluctuations. The role of singularities in phase transitions and a general topological classification of singularities is considered. Applications of the theory to magnets, liquid crystals, superfluids, superconductors and plasmas are demonstrated.
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V. L. Pokrovsky (1979) studied this question.
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