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Application of Algebraic Combinatorics to Finite Spin Systems with Dihedral Symmetry

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Bucikiewicz S., Dębski L., Florek W.

Acta Physica Polonica A

2001

vol. 100

issue 4

453-475

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.

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1 Acta Physica Polonica A

1 2001

1 Bucikiewicz S.

1 Dębski L.

1 Florek W.

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Application of Algebraic Combinatorics to Finite Spin Systems with Dihedral Symmetry