Condensed Matter Physics, 2017, vol. 20, No. 1, 13701
DOI:10.5488/CMP.20.13701           arXiv:1609.04990

Title: The large-m limit, and spin liquid correlations in kagome-like spin models
  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 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  – .

Key words: kagome lattice, frustration, spin correlations, exact result
PACS: 75.10.Hk, 05.50.+q, 75.25.+z, 75.40.Cx

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