Ising model with competing axial interactions in the presence of a field: A mean-field treatment

We study a layered Ising model with competing interactions between nearest and next-nearest layers in the presence of a magnetic field. The analysis is restricted to the mean-field approximation with one effective field for each layer. The high-temperature region is studied analytically. The $\lambda$ surface, separating the paramagnetic and the modulated phases, is bounded by two lines of tricritical points which join smoothly at the Lifshitz point and terminate at multicritical points, beyond which lines of critical and double critical end points are expected to appear. The magnetization structure near the $\lambda$ surface can be described as having an almost sinusoidal oscillation, with the higher harmonic components contributing as perturbations. Both odd and even higher-harmonic components are present in nonzero fields, and the $n$th harmonic component depends asymptotically on the $n$th power of the main harmonic component. The low-temperature region is studied numerically. We construct $T-H$ phase diagrams, which exhibit a variety of modulated phases, for various values of the ratio of the strength of the competing interactions.