Condensed Matter Physics, 2017, vol. 20, No. 1, 13701
The large-m limit, and spin liquid correlations in kagome-like spin models
(AMRC, Coventry University, CV1 5FB, United Kingdom)
It is noted that the pair correlation matrix 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 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 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 – in the opposite limits of m can imply their quasi-degeneracy
for intermediate 1≤m<∞. For an anti-ferromagnetic nearest
neighbor coupling, that renders kagome-like 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 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 – .
kagome lattice, frustration, spin correlations, exact result
75.10.Hk, 05.50.+q, 75.25.+z, 75.40.Cx