Nature of Long-Range Order in Stripe-Forming Systems with Long-Range Repulsive Interactions

We study two dimensional stripe forming systems with competing repulsive interactions decaying as $r^{-alpha}$. We derive an effective Hamiltonian with a short range part and a generalized dipolar interaction which depends on the exponent $alpha$. An approximate map of this model to a known XY model with dipolar interactions allows us to conclude that, for $alpha <2$ long range orientational order of stripes can exist in two dimensions, and establish the universality class of the models. When $alpha geq 2$ no long-range order is possible, but a phase transition in the KT universality class is still present. These two different critical scenarios should be observed in experimentally relevant two dimensional systems like electronic liquids ($alpha=1$) and dipolar magnetic films ($alpha=3$). Results from Langevin simulations of Coulomb and dipolar systems give support to the theoretical results.

The nematic phase in stripe forming systems within the self consistent screening approximation

We show that in order to describe the isotropic-nematic transition in stripe forming systems with isotropic competing interactions of the Brazovskii class it is necessary to consider the next to leading order in a 1/N approximation for the effective Hamiltonian. This can be conveniently accomplished within the self-consistent screening approximation. We solve the relevant equations and show that the self-energy in this approximation is able to generate the essential wave vector dependence to account for the anisotropic character of two-point correlation function characteristic of a nematic phase.