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2001 | 100 | 1 | 3-22
Article title

Application of Algebraic Combinatorics to Finite Spin Systems

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EN
Abstracts
EN
A finite spin system invariant under a symmetry group G is a very illustrative example of a finite group action on mappings f: X → Y (X is a set of spin carriers, Y contains spin projections for a given spin number s). Orbits and stabilizers are used as additional indices of the symmetry adapted basis. Their mathematical nature does not decrease a dimension of a given eigenproblem, but they label states in a systematic way. It allows construction of general formulas for vectors of symmetry adapted basis and matrix elements of operators commuting with the action of G in the space of states. The special role is played by double cosets, since they label nonequivalent (from the symmetry point of view) matrix elements ãx|H|yã for an operator H between Ising configurations |x〉,|y〉. Considerations presented in this paper should be followed by a detailed discussion of different symmetry groups (e.g.) cyclic or dihedral ones) and optimal implementation of algorithms. The paradigmatic example, i.e. a finite spin system, can be useful in investigations of magnetic macromolecules like Fe_6 or Mn_{12} acetate.
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Year
Volume
100
Issue
1
Pages
3-22
Physical description
Dates
published
2001-07
received
2001-06-11
(unknown)
2001-07-13
Contributors
author
  • Institute of Physics, A. Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland
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Document Type
Publication order reference
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bwmeta1.element.bwnjournal-article-appv100n107kz
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