Low-temperature series expansions for the square lattice Ising model with spin S > 1

We derive low-temperature series (in the variable u = exp[-βJ/S²]) for the spontaneous magnetization, susceptibility, and specific heat of the spin-S Ising model on the square lattice for S = 3/2, 2, 5/2, and 3. We determine the location of the physical critical point and non-physical singularities. The number of non-physical singularities closer to the origin than the physical critical point grows quite rapidly with S. The critical exponents at the singularities which are closest to the origin and for which we have reasonably accurate estimates are independent of S. Due to the many non-physical singularities, the estimates for the physical critical point and exponents are poor for higher values of S, though consistent with universality.