On exomorphic types of phase transitions

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 S_n. 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 C_4v¹ in BaTiO₃ and D_6h⁴ to D_2h¹⁶ in β-K ₂SO₄ are derived and it is shown that these two phase transitions belong to the same exomorphic type.