Generalization of the Luttinger-Tisza Method

Using permutation groups the Luttinger-Tisza method for the calculation of the low-temperature ordered state of spin configuratons is generalized to treat more than one ion per unit cell. It is found that, for the dipole-dipole interaction, not more than two ions per unit cell can be treated by this method. On the other hand, for the exchange interaction it is possible to treat the case of $2^m$ ions per unit cell ($m$ is an integer), provided the ions occupy special positions.