Frustrated Ising systems on Husimi trees

We consider two frustrated Ising model systems. The first is the full frustrated antiferromagnetic Ising model on the triangle lattice. We approximate the system by a Husimi tree. By a “sequential” build up of the tree we get a qualitatively correct phase diagram which quantitatively is close to other approximation methods. Most closed form approximations of this system such as mean field theory give qualitatively incorrect phase diagrams. As a further test of the Husimi tree approach we look at a frustrated Ising model on a checkerboard type lattice. This system has been solved exactly by Azaria et al., Phys. Rev. Lett. 59 (1987) 1629, when h=0. Again the Husimi tree approach gives qualitatively correct results approximating a rather complex phase diagram with e.g. reentrant phases. And in addition this approach allows one to determine the phase diagram for h≠0. Finally, this method should be easily extended to a number of other frustrated lattice spin systems such as the fully frustrated system on the simple cubic lattice.