The phase diagram of a bilayer Ising model

The phase diagram of a quasi-2D two-layer Ising lattice, with a variable inter-layer interaction parameter, is determined by phenomenological order-disorder, mean-field (MF), and simplified renormalization group (RG) approaches. Bethe approximation is used to determine phase diagrams of bond-diluted bilayer lattices, exhibiting non-trivial behavior in the presence of short-range correlations between the bonds. The critical behavior is discussed and the problem is shown to belong to the 2D-Ising universality class, for any given value of the inter-layer interaction. The phase diagram is verified by comparison to earlier results, obtained by computer simulations, perturbation series expansion, Bethe-tree approximation and other methods.