  We present a comprehensive Monte Carlo study of domain growth in the
random-bond XY model with non-conserved kinetics. The presence of quenched
disorder slows down domain growth in d = 2; 3. In d = 2, we observe power-law
growth with a disorder-dependent exponent on the time-scales of our simulation.
In d = 3, we see the signature of an asymptotically logarithmic growth regime.
The scaling functions for the real-space correlation function are seen to be
independent of the disorder. However, the same does not apply for the two-time
autocorrelation function, demonstrating the breakdown of superuniversality.
