  We investigate the nature of the phase transition occurring in a planar
XY-model spin system with dipole-dipole interactions. It is demonstrated that a
Berezinskii-Kosterlitz-Thouless (BKT) type of phase transition always takes
place at a finite temperature separating the ordered (ferro) and the disordered
(para) phases. The low-temperature phase corresponds to an ordered state with
thermal fluctuations, composed of a "gas" of bound vortex-antivortex pairs,
which would, when considered isolated, be characterized by a constant
vortex-antivortex attraction force which is due to the dipolar interaction term
in the Hamiltonian. Using a topological charge model, we show that small bound
pairs are easily polarized, and screen the vortex-antivortex interaction in
sufficiently large pairs. Screening changes the linear attraction potential of
vortices to a logarithmic one, and leads to the familiar pair dissociation
mechanism of the BKT type phase transition. The topological charge model is
confirmed by numerical simulations, in which we demonstrate that the transition
temperature slightly increases when compared with the BKT result for
short-range interactions.
