New type of exact solutions to the generalized Ashkin-Teller model and anisotropic Ising model with spin 3/2

The generalized Ashkin-Teller model involving both biquadratic and bilinear interactions between the Ising subsystems ($\alpha$ and $s$) and equivalent to the anisotropic Ising model with spin 3/2 is considered. For a certain magnitude of the opposite-sign bilinear interactions along the horizontal and vertical axes of a square lattice, the exact analytic solution is obtained that describes the phase transition between the disordered ($<\alpha>=<s>=<\alpha s>=0$) and the correlated ordered ($<s>\ne 0$ and $<\alpha>=<s>=0$) states.