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 $\alpha \ge 2$ 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.