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.
