We perform large-scale Monte Carlo simulations of the classical XY model on a three-dimensional $Ltimes L times L$ cubic lattice using the graphics processing unit (GPU). By the combination of Metropolis single-spin flip, over-relaxation and parallel
-tempering methods, we simulate systems up to L=160. Performing the finite-size scaling analysis, we obtain estimates of the critical exponents for the three-dimensional XY universality class: $alpha=-0.01293(48)$ and $ u=0.67098(16)$. Our estimate for the correlation-length exponent $ u$, in contrast to previous theoretical estimates, agrees with the most recent experimental estimate $ u_{rm exp}=0.6709(1)$ at the superfluid transition of $^4$He in a microgravity environment.
