Absence of Reentrance in the Two-Dimensional XY-Model with Random Phase Shift

(Received 10 January 1995, received in final form 25 January 1995, accepted 27 January 1995)

Abstract
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 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 the independent dipole approximation. 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.