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High-precision Monte Carlo study of the three-dimensional XY model on GPU

We perform large-scale Monte Carlo simulations of the classical XY model on a three-dimensional $L\times L \times L$ 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: $α=-0.01293(48)$ and $ν=0.67098(16)$. Our estimate for the correlation-length exponent $ν$, in contrast to previous theoretical estimates, agrees with the most recent experimental estimate $ν_{\rm exp}=0.6709(1)$ at the superfluid transition of $^4$He in a microgravity environment.