The methods of calculating Curie temperatures used by Opechowski and Weiss are extended to higher spin values. Using the former, Curie temperatures are found for the face-centered, body-centered, and simple cubic and the hexagonal and quadratic layer lattices for spin ½ to 3. Weiss' method is applied to the body-centered and simple cubics for spin ½ to 2 and to the quadratic layer lattice for spin ½ and 1. Numerical results show good agreement between the two methods for three-dimensional ferromagnetic lattices. However, the Opechowski method fails to locate the antiferromagnetic transition and predicts a transition for the two-dimensional lattices while the Weiss method does not. A classical-spin approximation is investigated and is found to give Curie temperatures within a few percent of the quantum-mechanical results for spin 1 or greater.

• Received 7 July 1955

DOI:https://doi.org/10.1103/PhysRev.100.685