Modulated Phases in the Simple Hexagonal Ising Lattice with Competing Interactions

Abstract

The phase diagram of the Ising model on the simple hexagonal lattice with competing interactions is studied within the mean-field approximation. The stability analysis of a paramagnetic phase shows that the present model exhibits a Lifshitz point separating the paramagnetic phase, an antiferromagnetic phase and a modulated phase. Numerical calculations are performed to investigate a gross feature of the phase diagram. It is shown that a large number of high-order commensurate phases are stable. The resulting phase diagram is strikingly different from the corresponding phase diagram of the axial next-nearest neighbor Ising (ANNNI) model.