Properties of ordered,continuously degenerate systems

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.