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