Abstract
We study duality transformations of the star–square relation and the generalized star–triangle relation for Ising-like lattice spin models. The lattice spin models are obtained via gauge/YBE correspondence which connects the supersymmetric gauge theories and lattice spin models of statistical mechanics. By the use of integral identities coming from the duality of three-dimensional supersymmetric gauge theories, we construct hyperbolic, lens hyperbolic, trigonometric, and rational solutions to the duality transformations. These duality transformations allow us to construct spin lattice models with four-spin (the star–square relation) and three-spin (the generalized star–triangle relation) interactions.
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