Phase diagram and critical points for a metamagnetic Ising model using constant coupling approximation

We compute the isotherms and phase diagram in the constant coupling approximation for an Ising metamagnet with various values for the ratio of the ferromagnetic to the antiferromagnetic coupling parameters. The constant coupling method is set up entirely with the internal fields as the variation parameter. The search for the tricritical point, both directly and indirectly via the hessian of the internal fields led to the conclusion that this model has no tricritical point, but a critical end point. Comparing our computation with the experimental result for FeBr2, we find that the value for the critical end point lies closer to the experiment than either the molecular field theory or the random phase approximation.