ABSENCE OF REENTRANCE IN THE 2-DIMENSIONAL XY-MODEL WITH RANDOM PLEASE SHIFT

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, a nd that the transition to the disordered phase is not reentrant. These results are obtained by heuristic arguments, an analytical renormaliz ation group calculation, and a numerical Migdal-Kadanoff renormalizati on group treatment. Previous predictions of reentrance are found to fa il due to an overestimation of the vortex pair density as a consequenc e of the independent dipole approximation. At positions where vortex p airs are energetically favored by disorder, their statistics becomes e ffectively fermionic. The results may have implications for a large nu mber of related models.