The bilayer Ising model and a generalized Husimi tree approximation

We study a variety of aspects of a bilayer system of Ising spins including accurate estimates of the critical temperature for ferromagnetic interactions, scaling of the critical temperature when the interlayer interaction goes to zero, and approximations of phase diagrams for the case when antiferromagnetic interlayer interactions are present including location of the tricritical point. This is all done using an extension of a method previously developed by the author to study a variety of lattice spin systems and which is a generalization of the Bethe lattice approach.