Planar rotator system in two dimensions with long-range interactions

Abstract

We study the two-dimensional (2D) planar rotator model with ferromagnetic long-range interactions decaying as r − p using the self-consistent harmonic approximation. We show that the overall behavior of the model approaches the one expected for nearest-neighbor model as p → ∞. The results obtained for the transition temperature are in agreement with Monte Carlo results reported in the literature. We check some asymptotic expressions currently used in the literature and propose a different expression for the case p = 4.