Application of Algebraic Combinatorics to Finite Spin Systems with Dihedral Symmetry |

S. Bucikiewicz, L. Dębski and W. FlorekInstitute of Physics, A. Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland |

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Received: June 11, 2001; in final form July 13, 2001 |

Properties of a given symmetry group G are very important in
investigation of a physical system invariant under its action. In the
case of finite spin systems (magnetic rings as Fe_{6}, Cu_{6}, Fe_{10}, some planar macromolecules as Fe_{12} or Fe_{8}) the symmetry group is isomorphic with the dihedral group D_{N}.
In this paper group-theoretical "parameters" of such groups are
determined, especially decompositions of transitive representations
into irreducible ones and double cosets. These results are necessary to
construct matrix elements of any operator commuting with G in an
efficient way. The approach proposed can be useful in many branches of
physics, but here it is applied to finite spin systems, which serve as
models for mesoscopic magnets. |

DOI: 10.12693/APhysPolA.100.453 PACS numbers: 02.20.Bb, 75.10.Jm, 75.75.+a |