An algorithmic method is presented to determine the irreducible representations that engender the irreducible representations associated with phase transitions involving a change of symmetry to a subgroup of index n. This method is based on the work of Ascher and Kobayashi [E. Ascher and J. Kobayashi, J. Phys. C 10, 1349 (1977)] and the derivation of faithful irreducible representations contained in the permutation representation of transitive subgroups of permutation groups Sn. Character tables of all such irreducible representations, and their epikernels, associated with a change in symmetry to a subgroup of index n = 2, 3, 4, 5, and 6 are given explicitly. The relationship to exomorphic types of phase transitions is then discussed. The irreducible representations associated with the phase transitions O h1 to C4v1 in BaTiO3 and D6h4 to D2h16 in β-K 2SO4 are derived and it is shown that these two phase transitions belong to the same exomorphic type.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics