Spin-32 ising model and two-layer Ising model

We present a spin-32 Ising model which is equivalent to a “two-layer” Ising model. We find a solvable spin-32 Ising model and show that a system may have several critical exponents η corresponding to correlation functions of different Ising-type variables. We find two phase-transition temperatures in some of the systems and clarify the nature of phases. In a system with competing antiferromagnetic and ferromagnetic interactions on a triangular lattice, there are two critical temperatures and the value of η is 14 at a finite critical temperature and 12 at the critical zero temperature. We calculate the critical temperature as a function of ratio of interactions by using the interfacial approximation for a system with competing antiferromagnetic and ferromagnetic interactions on a square lattice; it turns out that the shift exponent is 0.5.