2 00 9 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 spinS 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) and only nearest-neighbor interaction, allow us to map this system either onto a purely spin-1/2 lattice or onto a purely spinS lattice. By imposing the condition that the mixed half-odd-integer spin-(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 spinS is given by S + 1/2. Therefore we conclude that this transformation is equivalent to a simple spin transformation which is independent of the coordination number. Two-dimensional lattice models are one of the most interesting subjects of statistical mechanics, both experimentally[1, 2] and theoretically. Several approximation methods are used to investigate these models on the lattice, such as mean-field theory[1, 3], the Bethe approximation[4], the correlated effective field theory[5], the renormalization group[6], series expansion methods[7], Monte Carlo methods[8] and cluster variation methods. Following Onsager's[9] solution for the square two dimensional Ising lattice, other solutions for regular