Abstract

We find the critical surface of the Ashkin–Teller model on the generic iso-radial graphs byusing the results for the anisotropic Ashkin–Teller model on the square lattice. Differentgeometrical aspects of this critical surface are discussed, especially their connectionto the anisotropy angle. The free energy of the model on the generic iso-radialgraph is extracted using the inversion identities. In addition, lattice holomorphicvariables are discussed at some particular points of the critical line. We check ourconjectures numerically for the anisotropic triangular lattice Ashkin–Teller model.

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