  We show, that the 2D XY-model with random phase shifts exhibits for low
temperature and small disorder a phase with quasi-long-range order, and that
the transition to the disordered phase is {\it not} reentrant. These results
are obtained by heuristic arguments, an analytical renormalization group
calculation, and a numerical Migdal-Kadanoff renormalization group treatment.
Previous predictions of reentrance are found to fail due to an overestimation
of the vortex pair density as a consequence of independent dipole
approximations. At positions, where vortex pairs are energetically favored by
disorder, their statistics becomes effectively fermionic. The results may have
implications for a large number of related models.
