The large-m limit, and spin liquid correlations in kagome-like spin models

It is noticed 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 noticed 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

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