The antiferromagnetic Ising model for a bilayer Bethe lattice

The totally antiferromagnetic Ising model is analyzed on a bilayer Bethe lattice in detail by studying the order-parameters, response functions, i.e. susceptibility and specific heat, and free energy by using the recursion relations in a pairwise approach. The ground state phase diagrams of the model are also obtained on the (J2/|J1|,J3/q|J1|)(J2/|J1|,J3/q|J1|) plane for given values of H/q|J1|H/q|J1| and on the (H/q|J1|,J3/q|J1|)(H/q|J1|,J3/q|J1|) plane for given J2/|J1|J2/|J1|. As a result, we have obtained the temperature-dependent phase diagrams for various values of the coordination number q   on the (J3/|J1|,kT/|J1|)(J3/|J1|,kT/|J1|) and (H/|J1|,kT/|J1|)(H/|J1|,kT/|J1|) planes for given values of the rest of the system parameters.