Following the preceding papers, the present paper is also concerned with homophone sequences of phase transitions, but assumes the soft modes more concretely to be of wavenumber zero. For every possible specification of both the point group of the prototypic phase and the irreducible representation for the soft modes, the pedigree is determined. Discussions are made about three typical cases in which the soft modes are threefold degenerate.
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Kêitsirô Aizu (1976) studied this question.
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