Combinatorial Structures in Spin Models: Algorithms for Generation of Operator Matrices

Florek, Wojciech

doi:10.12921/cmst.2001.07.01.41-54

Cited by 2 publications

(1 citation statement)

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“…The last one consists in efficient implementation of proposed algorithms, working-out methods of storing of configuration etc. These problems have been recently presented elsewhere, 31,39,40 so they are left out in the present paper. The second and third steps are slightly modified standard procedures known since the famous paper of Bonner and Fisher 41 and reused lately in many articles, for example by Waldmann in Ref.…”

Section: Classification Of States By Means Of Algebraic Combinatoricsmentioning

confidence: 99%

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

Florek

Bucikiewicz

2002

Phys. Rev. B

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The spin correlations ω z r , r = 1, 2, 3, and the probability pN of finding a system in the Néel state for the antiferromagnetic ring Fe III 6 (the so-called 'small ferric wheel') are calculated. States with magnetization M = 0, total spin 0 ≤ S ≤ 15 and labeled by two (out of four) one-dimensional irreducible representations (irreps) of the point symmetry group D6 are taken into account. This choice follows from importance of these irreps in analyzing low-lying states in each S-multiplet. Taking into account the Clebsch-Gordan coefficients for coupling total spins of sublattices (SA = SB = 15 2 ) the global Néel probability p * N can be determined. Dependencies of these quantities on state energy (per bond and in the units of exchange integral J) and the total spin S are analyzed. Providing we have determined pN(S) etc. for other antiferromagnetic rings (Fe10, for instance) we could try to approximate results for the largest synthesized ferric wheel Fe18. Since thermodynamic properties of Fe6 have been investigated recently, in the present considerations they are not discussed, but only used to verify obtained values of eigenenergies. Numerical results are calculated with high precision using two main tools: (i) thorough analysis of symmetry properties including methods of algebraic combinatorics and (ii) multiple precision arithmetic library GMP. The system considered yields more than 45 thousands basic states (the so-called Ising configurations), but application of the method proposed reduces this problem to 20-dimensional eigenproblem for the ground state (S = 0). The largest eigenproblem has to be solved for S = 4; its dimension is 60. These two facts (high precision and small resultant eigenproblems) confirm efficiency and usefulness of such an approach, so it is briefly discussed here.

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Section: Classification Of States By Means Of Algebraic Combinatoricsmentioning

confidence: 99%