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

TL;DR

This Monte Carlo study investigates the phase transitions of the 2D XY model with quenched random phases, revealing a critical disorder level where a transition occurs and challenging some existing theories about low-temperature phases.

Contribution

The paper provides the first detailed phase diagram and critical behavior analysis of the 2D XY model with quenched disorder using Monte Carlo simulations.

Findings

Existence of a KT transition for disorder below a critical value

Quasi-long-range order persists down to T=0 contrary to some theories

Disorder-driven unbinding of vortex pairs at the transition point

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 $T_{KT}\rightarrow 0$ 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.