J. Phys. I France
Volume 5, Numéro 5, May 1995
Page(s) 565 - 572
DOI: 10.1051/jp1:1995152
J. Phys. I France 5 (1995) 565-572

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

Thomas Nattermann1, Stefan Scheidl1, Sergey E. Korshunov2 and Mai Suan Li3

1  Institut für Theoretishe Physik, Universität zu Köln, Köln, Germany
2  Landau Institute for Theoretical Physics, Kosygina 2, 117940 Moscow, Russia
3  Institute of Physics, 02-668 Warsaw, Poland

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

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.

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