2020
DOI: 10.48550/arxiv.2002.12705
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Theory of ground states for classical Heisenberg spin systems V

Heinz-Jürgen Schmidt,
Wojciech Florek

Abstract: We formulate part V of a rigorous theory of ground states for classical, finite, Heisenberg spin systems. After recapitulating the central results of the parts I -IV previously published we extend the theory to the case where an involutary symmetry is present and the ground states can be distinguished according to their degree of mixing components of different parity. The theory is illustrated by a couple of examples of increasing complexity.

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Cited by 3 publications
(6 citation statements)
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“…We will analytically calculate the saturation susceptibility and check it by numerical calculations. This example has also be considered in [22] with a general ferromagnetic bond strength. Its homogeneously gauged J-matrix has the form…”
Section: Almost Regular Cubementioning
confidence: 99%
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“…We will analytically calculate the saturation susceptibility and check it by numerical calculations. This example has also be considered in [22] with a general ferromagnetic bond strength. Its homogeneously gauged J-matrix has the form…”
Section: Almost Regular Cubementioning
confidence: 99%
“…Here we have adopted the notation Root [p(x), n] for the nth root of the polynomial p(x) analogous to the similar MATHEMATICA command. In passing we note the special form of ξ with alternating components due to the reflectional symmetry of the almost regular cube, see [22] for details. We conclude…”
Section: B Isosceles Trianglementioning
confidence: 99%
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“…Our approach will be based on the 'Lagrange-variety theory' of classical ground states given in [6,11,[19][20][21][22][23] which is intended to apply to general Heisenberg systems and is not specifically tailored for spin lattices. The basic result of this theory is that the ground states can be constructed by superpositions of the eigenvectors corresponding to the minimal eigenvalue not of the original J-matrix but of the 'dressed J-matrix'.…”
Section: Introductionmentioning
confidence: 99%
“…The paper is organized as follows. In section 2.1 we recapitulate the general definitions and results that have already appeared in [6,11,[19][20][21][22][23], while the specializations to spin lattices are presented in section 2.2. The proofs of two propositions appearing in this section are moved to the appendix.…”
Section: Introductionmentioning
confidence: 99%