The large-m limit, and spin liquid correlations in kagome-like spin models
It is noted that the pair correlation matrix χˆ of the nearest neighbor Ising model on periodic three-dimensional (d = 3) kagome-like lattices of corner-sharing triangles can be calculated partially exactly. Specifically, a macroscopic number 1/3N + 1 out of N eigenvalues of χˆ are degenerate at al...
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| Date: | 2017 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут фізики конденсованих систем НАН України
2017
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| Series: | Condensed Matter Physics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/156978 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The large-m limit, and spin liquid correlations in kagome-like spin models / T. Yavors'kii // Condensed Matter Physics. — 2017. — Т. 20, № 1. — С. 13701: 1–7. — Бібліогр.: 25 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | It is noted that the pair correlation matrix χˆ of the nearest neighbor Ising model on periodic three-dimensional
(d = 3) kagome-like lattices of corner-sharing triangles can be calculated partially exactly. Specifically, a macroscopic number 1/3N + 1 out of N eigenvalues of χˆ are degenerate at all temperatures T , and correspond to
an eigenspace L− of χˆ, independent of T . Degeneracy of the eigenvalues, and L− are an exact result for a
complex d = 3 statistical physical model. It is further noted that the eigenvalue degeneracy describing the same
L− is exact at all T in an infinite spin dimensionality m limit of the isotropic m-vector approximation to the
Ising models. A peculiar match of the opposite m = 1 and m → ∞ limits can be interpreted that the m → ∞
considerations are exact for m = 1. It is not clear whether the match is coincidental. It is then speculated that
the exact eigenvalues degeneracy in L− in the opposite limits of m can imply their quasi-degeneracy for intermediate 1 É m < ∞. For an anti-ferromagnetic nearest neighbor coupling, that renders kagome-like models
highly geometrically frustrated, these are spin states largely from L− that for m Ê 2 contribute to χˆ at low T .
The m → ∞ formulae can be thus quantitatively correct in description of χˆ and clarifying the role of perturbations in kagome-like systems deep in the collective paramagnetic regime. An exception may be an interval of T ,
where the order-by-disorder mechanisms select sub-manifolds of L−. |
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