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The large-m limit, and spin liquid correlations in kagome-like spin models | | Taras Yavors'kii
; | | Date: |
16 Sep 2016 | | Abstract: | It is noticed that the pair correlation matrix chi 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 1/3 N+1 out of N eigenvalues of chi are degenerate at all
temperatures T, and correspond to an eigenspace L_ of chi, independent of T.
Degeneracy of the eigenvalues, and L_ are an exact result for a complex d=3
statistical physical model.
It is further noticed 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->infinity limits can be interpreted that the m->infinity
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<=m<infinity. 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>=2 contribute to chi at low T. The
m->infinity formulae can be thus quantitatively correct in description of chi
and determination of 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_. | | Source: | arXiv, 1609.4990 | | Services: | Forum | Review | PDF | Favorites | |
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