The one-dimensional Ising model is investigated by generalizing the Bethe approximation, which, in this case, gives exact solutions. The energy, specific heat and the zero field susceptibility for S=1, 3/2 and 2 except the susceptibility for S=2 are calculated exactly and compared with the results of Suzuki et al. As a direct application of this method, the special lattice called the Bethe lattice is treated, and the Curie temperature of the lattice for S=1 is obtained. This method is also applied to solve the one-dimensional Ising model with the second neighbor interactions as well as the first neighbor ones, and the energy and specific heat for S=1/2 are calculated. © 1968, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.
