Abstract
On the basis of exact analytical solutions for spin-spin correlation functions in the one-dimensional 3-state [1] and 4-state [2] standard Potts models and Ising model [3] with allowance for the interactions between nearest neighbors J and next-nearest neighbors J′, phenomena of the appearance and disappearance of frustrations have been investigated, depending on the signs of J and J′ and the ratio of the interactions. In the Ising model, these phenomena have been studied on triangular, hexagonal, and kagome lattices on the basis of exact analytical solutions for the maximum values of the Kramers-Wannier matrices obtained in [4, 5].
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