XY model in small-world networks

The phase transition in the $\mathrm{XY}$ model on one-dimensional small-world networks is investigated by means of Monte Carlo simulations. It is found that long-range order is present at finite temperatures, even for very small values of the rewiring probability, suggesting a finite-temperature transition for any nonzero rewiring probability. Nature of the phase transition is discussed in comparison with the globally coupled $\mathrm{XY}$ model.