An analytic approach to Ising model with spin 12 and spin 1

An analytic method that applies to the spin 12 and 1 Ising models is used to calculate the transition temperatures. This method is based on a reduction scheme for certain well defined higher-order correlations. The completely new formulation removes the discrepancies occuring in the correlation reduction theory developed previously by Zhang. The estimation of the critical points for the spin 12 and 1 Ising models on the cubic lattices is compatible with series expansions to within 1.69% and 0.15%, respectively. The extension of the method to arbitrary spin is straightforward.