  In this work we have used extensive Monte Carlo calculations to study the
planar to paramagnetic phase transition in the two-dimensional anisotropic
Heisenberg model with dipolar interactions (AHd) considering the true
long-range character of the dipolar interactions by means of the Ewald
summation. Our results are consistent with an order-disorder phase transition
with unusual critical exponents in agreement with our previous results for the
Planar Rotator model with dipolar interactions. Nevertheless, our results
disagrees with the Renormalization Group results of Maier and Schwabl [PRB, 70,
134430 (2004)] and the results of Rapini et. al. [PRB, 75, 014425 (2007)],
where the AHd was studied using a cut-off in the evaluation of the dipolar
interactions. We argue that besides the long-range character of dipolar
interactions their anisotropic character may have a deeper effect in the system
than previously believed. Besides, our results shows that the use of a cut-off
radius in the evaluation of dipolar interactions must be avoided when analyzing
the critical behavior of magnetic systems, since it may lead to erroneous
results.
