Mean-field calculations for the axial next-nearest-neighbor Ising model in a random field

Abstract

We consider a mean-field version of an Ising model on a simple cubic lattice with competing interactions between nearest and next-nearest neighbors along the $z$ axis in the presence of a random field. We obtain phase diagrams in terms of the temperature, the ratio of the strengths of the competing interactions, and the intensity of the $\ifmmode\pm\else\textpm\fi{}H$ random fields. There are no drastic qualitative changes for weak random fields. The effect of moderate random fields consists in the change of order of the transitions to the disordered phase. Although the transition from the paramagnetic to the ordered (ferromagnetic and modulated) phases in the absence of a random field is always continuous, for random fields of moderate intensity we show the appearance of tricritical points separating the critical lines (at higher temperatures) from a line of first-order transitions (at lower temperatures). We show the presence of modulated phases with disordered layers (with zero magnetization) and the pinching of the corresponding regions in the phase diagram. The modulated structures are destroyed in the presence of strong random fields.