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We show that the equality of 2d $\mathcal{N}$=(2,2) supersymmetric indices inSeiberg-type duality leads to a new integrable Ising-type model. The emergenceof the new model is the result of correspondence between the supersymmetric$SU(2)$ quiver gauge theories and the Yang-Baxter equation. Using thiscorrespondence, we solve the star-triangle relation and obtain thetwo-dimensional exactly solvable spin model. The model corresponding to oursolution possesses continuous spin variables on the circle and the Boltzmannweights are demonstrated in terms of Jacobi theta function. Using the solutionof the star-triangle relation, we also construct interaction-round-a-face andvertex models.

A New Integrable Ising-type Model from 2d $\mathcal{N}$=(2,2) Dualities