The Kramers-Wannier duality as the Tutte type duality

Kramers-Wannier duality is a well-established technique for deriving an explicit equation for the critical temperature of the Potts model on a planar square lattice. Furthermore, it provides a relation between the critical temperatures of Potts models on a planar lattice $G$ and its dual lattice $G^*$.This talk focuses on the derivation of Kramers-Wannier duality through the Tutte duality, exploiting the inherent connection between Potts models and Tutte polynomials. This approach proves to be highly effective, as it offers a generalized algebraic perspective that potentially enables the extension of this duality to Potts models on non-planar lattices.