Classification of continuous phase transitions and stable phases. II. Four-dimensional order parameters.

%e have classified continuous phase transitions in physical systems where the order parameter transforms as a four-dimensional representation of a three-dimensional space group. For most active four-dimensional space-group representations the "phase diagrams" are obtained. %'e also give prescriptions to lift the degeneracy, occurring at the fourth-degree polynomical expansion of the free energy, between phases preserving maximal isotropy subgroups and to distinguish images yielding the same quartic potential. In two cases we have found that the symmetry is reduced to the minimal one after the phase transition.