Condensed Matter Physics, 2017, vol. 20, No. 1, 13701
DOI:10.5488/CMP.20.13701
arXiv:1609.04990
Title:
The largem limit, and spin liquid correlations in kagomelike spin models
Author(s):

T. Yavors'kii
(AMRC, Coventry University, CV1 5FB, United Kingdom)

It is noted that the pair correlation matrix of the nearest neighbor Ising model on periodic threedimensional (d=3) kagomelike
lattices of cornersharing triangles can be calculated
partially exactly. Specifically, a macroscopic number 1/3N+1 out of N eigenvalues of are degenerate at all temperatures
T, and correspond to an eigenspace _{ –}
of , independent of T. Degeneracy of the eigenvalues, and
_{ –} are an exact result for a complex d=3
statistical physical model. It is further noted that the eigenvalue
degeneracy describing the same _{ –} is exact at all T in an infinite spin dimensionality m limit of the
isotropic mvector 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 _{ –} in the opposite limits of m can imply their quasidegeneracy
for intermediate 1≤m<∞. For an antiferromagnetic nearest
neighbor coupling, that renders kagomelike models highly geometrically frustrated, these are spin states largely from _{ –}
that for m≥2 contribute to
at low T.
The m→ ∞ formulae can be thus quantitatively correct in description of and clarifying the role of perturbations
in kagomelike systems deep in the collective paramagnetic regime.
An exception may be an interval of T, where the orderbydisorder mechanisms select submanifolds of _{ –} .
Key words:
kagome lattice, frustration, spin correlations, exact result
PACS:
75.10.Hk, 05.50.+q, 75.25.+z, 75.40.Cx
