On the three-sublattice random antiferromagnet

Abstract Some properties of a model for random antiferromagnets with a three-sublattice structure (Ising model) which is a generalization of the well-known Sherrington–Kirkpatrick model are studied. Using standard techniques, we obtain the replica symmetric and permutation broken replica symmetry (RSB) solutions (numerically) and the phase diagram in the field versus temperature plane. The solution indicates that metastability is greatly enhanced in many sublattice systems as compared with simple systems. It is found that there may appear two kinds of RSB solutions for some values of the temperature and external field one of them with a Parisi's order-parameter function displaying non-monotonic behavior.