Numerical study of 2D ANNNI model in the cluster variation method

An approximation in the cluster variation method (CVM) is used to investigate the modulated phases as well as the critical temperatures of the 2D and the 3D ANNNI models. It is first found that it shows the existence and the non-existence of the Lifshitz points in the 3D and the 2D model, respectively. In the second place, the free energies of periodic solutions in the modulated phases of the 2D ANNNI model are calculated under the periodic boundary condition that the system has 88 layers in the direction of the competing interactions, and it is concluded from the result that the 2D ANNNI model is always in an incommensurate phase in the modulated phase by this method.