The phase diagram of simple metamagnets as determined by the cluster variation method

In order to explore the global properties of a simple Ising metamagnet we computed the values of the coupling parameters for which the tricritical behavior is replaced by bicritical endpoints (Lifshitz point). The transition points are determined by means of the cluster variation method. The metamagnets studied have an antiferromagnetic coupling between the spins on two chosen sublattices and a ferromagnetic coupling between spins on the same sublattice. The following lattices and sublatices were considered: two-dimensional square, simple cubic and two different subdivisions of the fcc and bcc lattices each. The method used is based on the coincidence of two roots for the bicritical endpoints and of three roots for the tricritical point. In contrast to the molecular field and the pair approximation results, the presence or absence of the Lifshitz point depends on the lattice structure considered. We discuss the comparison of our results with the results from the renormalization theories.