The two-dimensional XY model with random phase shifts on bonds is studied. The analysis is based on a renormalization group for the replicated system. The model is shown to have an ordered phase with quasi-long-range order. This ordered phase consists of a glasslike region at lower temperatures and of a nonglassy region at higher temperatures. The transition from the disordered phase into the ordered phase is not reentrant and is of a new universality class at zero temperature. In contrast to previous approaches the disorder strength is found to be renormalized to larger values. Several correlation functions are calculated for the ordered phase. They allow one to identify not only the transition into the glassy phase but also an additional crossover line, where the disconnected vortex correlation changes its behavior on large scales nonanalytically. The renormalization group approach yields the glassy features without a breaking of replica symmetry.
The generalized Trotter formula is used to map the two-dimensional spin-l/2 XY model onto a three-dimensional lsing model with complicated many-spin interactions. This relationship sused to construct an efficient Monte Carlo algorithm. Simulation data for the specific heat and vortex correlation functions give strong evidence for the existence of a phase transition. Although it is well known that there cannot exist long-range order in the two-dimensional (2D) spin-1/2 XY model at non-zero temperature [1], high-temper-ature series expansions [2] suggest he existence of critical behavior. Little is known about the quantum model mainly because most techniques which have been succesfully applied to the classical model (also referred to as planar rotator model) are very difficult to extend to the quantum case. In particular, quantum renormalization group analYsis of the 2D spin-1/2 XY model have given either contradictive or unreliable re-suits [3-8]. An alternative method to calculate the thermody-namic properties of this modelis to exploit the formal analogy between d-dimensional quantum spin systems and (d + 1)-dimensional Ising-spin models [9]. Using ~ ' This paper was first submitted to Physical Review Letters