Partially disordered states of the three-dimensional ANNNI model

We analyze the three-dimensional axial next-nearest-neighbor Ising model composed of two kinds of alternately stacked ferromagnetic layers with different intralayer interactions by using Monte Carlo (MC) simulation. The detailed analyses of the magnetization and the spin correlations perpendicular to the stacked direction, assure and clarify the existence and the nature of the paramagnetic layers in some modulated phases with wave numbers, 1 4 , 1 8 , 3 16 . This is the first MC confirmation of the partially disordered states which have been predicted by previous molecular field calculation and/or observed in materials such as CsCoCl 3, CuFeO 2 and CeSb.