Phase Transitions in the Two-Dimensional XY Model with Random Phases: a Monte Carlo Study

Abstract

We study the two-dimensional XY model with quenched random phases by Monte Carlo simulation and finite-size scaling analysis. We determine the phase diagram of the model and study its critical behavior as a function of disorder and temperature. If the strength of the randomness is less than a critical value, $σ_{c}$, the system has a Kosterlitz-Thouless (KT) phase transition from the paramagnetic phase to a state with quasi-long-range order. Our data suggest that the latter exists down to T=0 in contradiction with theories that predict the appearance of a low-temperature reentrant phase. At the critical disorder $T_{KT}\rightarrow 0$ and for $σ> σ_{c}$ there is no quasi-ordered phase. At zero temperature there is a phase transition between two different glassy states at $σ_{c}$. The functional dependence of the correlation length on $σ$ suggests that this transition corresponds to the disorder-driven unbinding of vortex pairs.