Me. Gouvea et Ast. Pires, PLANAR ROTATOR SYSTEM IN 2 DIMENSIONS WITH LONG-RANGE INTERACTIONS, Journal of magnetism and magnetic materials, 162(2-3), 1996, pp. 225-229
We study the two-dimensional (2D) planar rotator model with ferromagne
tic long-range interactions decaying as r(-p) using the self-consisten
t harmonic approximation. We show that the overall behavior of the mod
el approaches the one expected for nearest-neighbor model as p --> inf
inity. The results obtained for the transition temperature are in agre
ement with Monte Carlo results reported in the literature. We check so
me asymptotic expressions currently used in the literature and propose
a different expression for the case p = 4.