A set of exactly solvable Ising models with half-odd-integer spin

We present a set of exactly solvable Ising models, with half-odd-integer spin-S   on a square-type lattice including a quartic interaction term in the Hamiltonian. The particular properties of the mixed lattice, associated with mixed half-odd-integer spin-(S,1/2)(S,1/2) and only nearest-neighbor interaction, allow us to map this system either onto a purely spin-1/2 lattice or onto a purely spin-S   lattice. By imposing the condition that the mixed half-odd-integer spin-(S,1/2)(S,1/2) lattice must have an exact solution, we found a set of exact solutions that satisfy the free fermion condition of the eight vertex model. The number of solutions for a general half-odd-integer spin-S   is given by S+1/2S+1/2. Therefore we conclude that this transformation is equivalent to a simple spin transformation which is independent of the coordination number.