2002/10/31 by K. Baerwinkel, K. Bärwinkel, Heinz–Jürgen Schmidt +3 · 1 citation
Materials Science · Physics and Astronomy · #Magnetism in coordination complexes #Polyoxometalates: Synthesis and Applications #Porphyrin and Phthalocyanine Chemistry #cond-mat.mtrl-sci #cond-mat.stat-mech
paper · pdf · doi:10.1140/epjb/e2003-00168-5
published as Eur. Phys. J. B 33 (2003) 285 · 17 pages, 5 figures, submitted to Eur. Phys. J. B. More information at http://www.physik.uni-osnabrueck.de/makrosysteme/
arxiv created 2003/04/04 · openalex publication_date 2003/06/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Large spin systems as given by magnetic macromolecules or two-dimensional spin arrays rule out an exact diagonalization of the Hamiltonian. Nevertheless, it is possible to derive upper and lower bounds of the minimal energies, i.e. the smallest energies for a given total spin S. The energy bounds are derived under additional assumptions on the topology of the coupling between the spins. The upper bound follows from "n-cyclicity", which roughly means that the graph of interactions can be wrapped round a ring with n vertices. The lower bound improves earlier results and follows from "n-homogeneity", i.e. from the assumption that the set of spins can be decomposed into n subsets where the interactions inside and between spins of different subsets fulfill certain homogeneity conditions. Many Heisenberg spin systems comply with both concepts such that both bounds are available. By investigating small systems which can be numerically diagonalized we find that the upper bounds are considerably closer to the true minimal energies than the lower ones.