Helical order and its onset at the Lifshitz point

We study the helical phase and the Lifshitz point for a model system with competing ferromagnetic and antiferromagnetic interactions by using high-temperature series techniques. We locate the Lifshitz point, and we find the exponent that characterizes the vanishing of the wave vector ${\overrightarrow{\mathrm{q}}}_0$ associated with the helical phase as the Lifshitz point is approached. In the helical phase we determine the dependence of ${\overrightarrow{\mathrm{q}}}_0$ on the competing interactions, and we estimate the structure factor exponent.