- Tytuł:
- Application of Algebraic Combinatorics to Finite Spin Systems
- Autorzy:
- Florek, W.
- Powiązania:
- https://bibliotekanauki.pl/articles/2027429.pdf
- Data publikacji:
- 2001-07
- Wydawca:
- Polska Akademia Nauk. Instytut Fizyki PAN
- Tematy:
-
02.20.Bb
75.10.Jm
75.75.+a - Opis:
- 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$\text{}_{12}$ acetate.
- Źródło:
-
Acta Physica Polonica A; 2001, 100, 1; 3-22
0587-4246
1898-794X - Pojawia się w:
- Acta Physica Polonica A
- Dostawca treści:
- Biblioteka Nauki
Artykuł