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

Ti-Yen Lan, Yun-Da Hsieh, Ying-Jer Kao
Center of Theoretical Science and Department of Physics, National Taiwan University, Taipei 10607, Taiwan
arXiv:1211.0780 [cond-mat.stat-mech] (5 Nov 2012)
@article{2012arXiv1211.0780L,

   author={Lan}, T.-Y. and {Hsieh}, Y.-D. and {Kao}, Y.-J.},

   title={"{High-precision Monte Carlo study of the three-dimensional XY model on GPU}"},

   journal={ArXiv e-prints},

   archivePrefix={"arXiv"},

   eprint={1211.0780},

   primaryClass={"cond-mat.stat-mech"},

   keywords={Condensed Matter – Statistical Mechanics, Physics – Computational Physics},

   year={2012},

   month={nov},

   adsurl={http://adsabs.harvard.edu/abs/2012arXiv1211.0780L},

   adsnote={Provided by the SAO/NASA Astrophysics Data System}

}

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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 $nu=0.67098(16)$. Our estimate for the correlation-length exponent $nu$, in contrast to previous theoretical estimates, agrees with the most recent experimental estimate $nu_{rm exp}=0.6709(1)$ at the superfluid transition of $^4$He in a microgravity environment.
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