ABSENCE OF REENTRANCE IN THE TWO-DIMENSIONAL XY-MODEL WITH RANDOM PHASE SHIFT

TL;DR

This paper demonstrates that the 2D XY-model with random phase shifts exhibits a phase with quasi-long-range order at low temperatures and small disorder, and that the transition to the disordered phase is not reentrant, contrary to previous predictions.

Contribution

The study provides a combined heuristic, analytical, and numerical analysis showing the absence of reentrance in the phase transition of the disordered 2D XY-model, correcting earlier overestimations.

Findings

Existence of quasi-long-range order at low temperature and small disorder.

Transition to disordered phase is not reentrant.

Vortex pair statistics become effectively fermionic where energetically favored.

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 {\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.