### Abstract

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 _{h}^{1} to C_{4v}^{1} in BaTiO_{3} and D_{6h}^{4} to D_{2h}^{16} in β-K _{2}SO_{4} are derived and it is shown that these two phase transitions belong to the same exomorphic type.

Original language | English (US) |
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Pages (from-to) | 661-667 |

Number of pages | 7 |

Journal | Journal of Mathematical Physics |

Volume | 27 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 1986 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

*Journal of Mathematical Physics*,

*27*(3), 661-667. https://doi.org/10.1063/1.527221