Application of Algebraic Combinatorics to Finite Spin Systems with Dihedral Symmetry
S. Bucikiewicz, L. Dębski and W. Florek
Institute 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 Fe6, Cu6, Fe10, some planar macromolecules as Fe12 or Fe8) the symmetry group is isomorphic with the dihedral group DN. 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