We consider a Bravais lattice of spins interacting via isotropic exchange with arbitrary interaction parameters. Villain has shown that the free energy, in the molecular field approximation (MFA), is a local minimum when the spin configuration is a simple spiral. It is possible to prove, however, by a method analogous to that of Luttinger and Tisza, that the simple spiral provides an absolute minimum to the free energy in the MFA. This result rules out the possibility of obtaining with the MFA any phase transition in such a system, except at the ordering temperature.

• Received 28 May 1963

DOI:https://doi.org/10.1103/PhysRev.132.122