Competing Interactions, the Renormalization Group, and the Isotropic-Nematic Phase Transition

We discuss 2D systems with Ising symmetry and competing interactions at different scales. In the framework of the renormalization group, we study the effect of relevant quartic interactions. In addition to the usual constant interaction term, we analyze the effect of quadrupole interactions in the self-consistent Hartree approximation. We show that in the case of a repulsive quadrupole interaction, there is a first-order phase transition to a stripe phase in agreement with the well-known Brazovskii result. However, in the case of attractive quadrupole interactions there is an isotropic-nematic second-order transition with higher critical temperature.