### 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) |
---|---|

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 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

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

}

*Journal of Mathematical Physics*, vol. 27, no. 3, pp. 661-667. https://doi.org/10.1063/1.527221

**On exomorphic types of phase transitions.** / Litvin, Daniel Bernard; Fuksa, J.; Kopsky, V.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On exomorphic types of phase transitions

AU - Litvin, Daniel Bernard

AU - Fuksa, J.

AU - Kopsky, V.

PY - 1986/1/1

Y1 - 1986/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33644772796&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33644772796&partnerID=8YFLogxK

U2 - 10.1063/1.527221

DO - 10.1063/1.527221

M3 - Article

AN - SCOPUS:33644772796

VL - 27

SP - 661

EP - 667

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 3

ER -