Does quasi-long-range order in the two-dimensional XY model really surviveweak random phase fluctuations?

Effective theories for random critical points are usually non-unitary, and thus may contain relevant operators with negative scaling dimensions. To st udy the consequences of the existence of negative-dimensional operators, we consider the random-bond XY model. It has been argued that the XY model on a square lattice, when weakly perturbed by random phases, has a quasi-long -range ordered phase (the random spin wave phase) at sufficiently low tempe ratures. We show that infinitely many relevant perturbations to the propose d critical action for the random spin wave phase were omitted in all previo us treatments. The physical origin of these perturbations is intimately rel ated to the existence of broadly distributed correlation functions. We find that those relevant perturbations do enter the Renormalization Group equat ions, and affect critical behavior. This raises the possibility that the ra ndom XY model has no quasi-long-range ordered phase and no Kosterlitz-Thoul ess (KT) phase transition, (C) 1999 Elsevier Science B.V. All rights reserv ed.