Ising model with isotropic competing interactions in the presence of a field: A tricritical-Lifshitz-point realization

We consider a spin system with competing interactions that are isotropic with respect to the axes of a cubic lattice. On the basis of an ε expansion, we demonstrate that for small values of the external field H, the paramagnetic-to-modulated-phase transition remains first order. For larger fields, such a transition changes to a continuous one at a tricritical point. As one varies the wave vector ${\mathit{q}}_{\mathit{c}}$ that is related to the modulated phase, one finds a line of such tricritical points. We remark that such a line must end at a Lifshitz tricritical point at ${\mathit{q}}_{\mathit{c}}$=0.