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The spin correlations \omega^z_r, r=1,2,3, and the probability p_N$ offinding a system in the Neel state for the antiferromagnetic ring Fe(III)6 (theso-called `small ferric wheel') are calculated. States with magnetization M=0,total spin 0<=S<=15 and labeled by two (out of four) one-dimensionalirreducible representations (irreps) of the point symmetry group D_6 are takeninto account. This choice follows from importance of these irreps in analyzinglow-lying states in each S-multiplet. Taking into account the Clebsch--Gordancoefficients for coupling total spins of sublattices (SA=SB=15/2) the globalNeel probability p*_N can be determined. Dependencies of these quantities onstate energy (per bond and in the units of exchange integral J) and the totalspin S are analyzed. Providing we have determined p_N(S) etc. for otherantiferromagnetic rings (Fe10, for instance) we could try to approximateresults for the largest synthesized ferric wheel Fe18. Since thermodynamicproperties of Fe6 have been investigated recently, in the presentconsiderations they are not discussed, but only used to verify obtained valuesof eigenenergies. Numerical results re calculated with high precision using twomain tools: (i) thorough analysis of symmetry properties including methods ofalgebraic combinatorics and (ii) multiple precision arithmetic library GMP. Thesystem considered yields more than 45 thousands basic states (the so-calledIsing configurations), but application of the method proposed reduces thisproblem to 20-dimensional eigenproblem for the ground state (S=0). The largesteigenproblem has to be solved for S=4; its dimension is 60. These two facts(high precision and small resultant eigenproblems) confirm efficiency andusefulness of such an approach, so it is briefly discussed here.Comment: 13 pages, 7 figs, 5 tabs, revtex

physical review. b, condensed matter

Néel probability and spin correlations in some nonmagnetic and nondegenerate states of the hexanuclear antiferromagnetic ring<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Fe</mml:mi></mml:mrow><mml:mrow><mml:mn>6</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>:</mml:mo></mml:math>Application of algebraic combinatorics to finite Heisenberg spin systems

Néel probability and spin correlations in some nonmagnetic and nondegenerate states of the hexanuclear antiferromagnetic ringFe6:Application of algebraic combinatorics to finite Heisenberg spin systems