Onsager approximation and asymptotically exact solution of the Ashkin–Teller model

The Onsager approximation of the Ashkin–Teller model is constructed. In certain ranges of variation of the parameters of the model this approximation is asymptotically exact. In particular, for the isotropic model it gives the exact asymptotic behavior for the phase curves, and for the anisotropic model it gives the asymptotic behavior of the critical surfaces.