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For lattice size ≫|R|≫ lattice spacing these conditions lead to a four-spin interaction ∼ log |R| for two-dimensional models and ∼ 1/|R| for three-dimensional models.
In the three-dimensional model of—ref. (4),. these conditions lead to the 1/|R| interaction of note (7) For lattice size ≫ |R|≫ lattice spacing these conditions lead to a four-spin interaction ∼ log |R| for two-dimensional models and ∼ 1/|R| for three-dimensional models. which leads to the smearing-out obtained in this reference.
The four-spin interaction is highly anisotropic and exists only for spins on the same line of atoms in which case it is ∼ |R| in the range of note (7) For lattice size ≫ |R| ≫ lattice spacing these conditions lead to a four-spin interaction ∼ log |R| for two-dimensional models and ∼/|R| for three-dimensional models.
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Coplan, L.A. Solvable elastic ising model with an improved four-spin interaction. Lett. Nuovo Cimento 8, 531–536 (1973). https://doi.org/10.1007/BF02728172
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DOI: https://doi.org/10.1007/BF02728172