Nature of long-range order in stripe-forming systems with long-range repulsive interactions

Abstract

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