Application of Algebraic Combinatorics to Finite Spin Systems with Dihedral Symmetry

• Authors: S. Bucikiewicz , L. Dębski , W. Florek
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

02.20.Bb; 75.10.Jm; 75.75.+a

Discipline

• 02.20.Bb: General structures of groups
• 75.10.Jm: Quantized spin models, including quantum spin frustration

• Journal: Acta Physica Polonica A
• Year: 2001
• Volume: 100
• Issue: 4
• Pages: 453-475

Dates

published

2001-10

received

2001-06-11

(unknown)

2001-07-13

Contributors

author

S. Bucikiewicz

• Institute of Physics, A. Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland

author

L. Dębski

• Institute of Physics, A. Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland

author

W. Florek

• Institute of Physics, A. Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland

References

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Identifiers

DOI

10.12693/APhysPolA.100.453