The Four-Dimensional XY Spin Glass

The nearest-neighbour XY spin glass on a hypercubic lattice in four dimensions is studied by Monte Carlo simulations. A finite- size scaling analysis of the data leads to a finite temperature spin glass transition at $T_c=0.95\pm 0.15$. The critical exponents are estimated to be $\nu_{sg}=0.70\pm 0.10$ and \eta_{sg}=-0.28\pm 0.38$. The results imply that the lower critical dimensionality for the XY spin glass is less than four.