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, ${\sigma }_c$, 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 $T_{KT}\to 0$ and for $\sigma >{\sigma }_c$ there is no quasi-ordered phase. At zero temperature there is a phase transition between two different glassy states at ${\sigma }_c$. The functional dependence of the correlation length on $\sigma$ suggests that this transition corresponds to the disorder-driven unbinding of vortex pairs.

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