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.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.

arXiv:1211.0780Nov 5, 20123 citations

Accelerating Quantum Monte Carlo via Graphics Processing Units

Benjamin Himberg, Adrian Del Maestro

An exact quantum Monte Carlo algorithm for interacting particles in the spatial continuum is extended to exploit the massive parallelism offered by graphics processing units. Its efficacy is tested on the Calogero-Sutherland model describing a system of bosons interacting in one spatial dimension via an inverse square law. Due to the long range nature of the interactions, this model has proved difficult to simulate via conventional path integral Monte Carlo methods running on conventional processors. Using Graphics Processing Units, optimal speedup factors of up to 640 times are obtained for N = 126 particles. The known results for the ground state energy are confirmed and, for the first time, the effects of thermal fluctuations at finite temperature are explored.An exact quantum Monte Carlo algorithm for interacting particles in the spatial continuum is extended to exploit the massive parallelism offered by graphics processing units. Its efficacy is tested on the Calogero-Sutherland model describing a system of bosons interacting in one spatial dimension via an inverse square law. Due to the long range nature of the interactions, this model has proved difficult to simulate via conventional path integral Monte Carlo methods running on conventional processors. Using Graphics Processing Units, optimal speedup factors of up to 640 times are obtained for N = 126 particles. The known results for the ground state energy are confirmed and, for the first time, the effects of thermal fluctuations at finite temperature are explored.

Bulletin of the American Physical SocietyMar 5, 20180 citations

Aging at the spin-glass/ferromagnet transition: Monte Carlo simulations using graphics processing units

Markus Manssen, Alexander K. Hartmann

We study the nonequilibrium aging behavior of the $\ifmmode\pm\else\textpm\fi{}J$ Edwards-Anderson model in three dimensions for samples of size up to $N={128}^{3}$ and for up to ${10}^{8}$ Monte Carlo sweeps. In particular we are interested in the change of the aging when crossing from the spin-glass phase to the ferromagnetic phase. The necessary long simulation times are reached by employing a CUDA-based GPU implementation, which allows for single-spin flip times as small as 8 ps. We measure typical spin-glass correlation functions in space and time to determine the growing length scale and extract the constituting exponents. We observe a clear signature of the disorder-driven equilibrium transition in the nonequilibrium behavior.We study the nonequilibrium aging behavior of the $\ifmmode\pm\else\textpm\fi{}J$ Edwards-Anderson model in three dimensions for samples of size up to $N={128}^{3}$ and for up to ${10}^{8}$ Monte Carlo sweeps. In particular we are interested in the change of the aging when crossing from the spin-glass phase to the ferromagnetic phase. The necessary long simulation times are reached by employing a CUDA-based GPU implementation, which allows for single-spin flip times as small as 8 ps. We measure typical spin-glass correlation functions in space and time to determine the growing length scale and extract the constituting exponents. We observe a clear signature of the disorder-driven equilibrium transition in the nonequilibrium behavior.

arXiv:1411.5512Physical Review BMay 26, 201518 citations

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.

We study the nonequilibrium aging behavior of the $\ifmmode\pm\else\textpm\fi{}J$ Edwards-Anderson model in three dimensions for samples of size up to

N={128}^{3}

and for up to

{10}^{8}

Monte Carlo sweeps. In particular we are interested in the change of the aging when crossing from the spin-glass phase to the ferromagnetic phase. The necessary long simulation times are reached by employing a CUDA-based GPU implementation, which allows for single-spin flip times as small as 8 ps. We measure typical spin-glass correlation functions in space and time to determine the growing length scale and extract the constituting exponents. We observe a clear signature of the disorder-driven equilibrium transition in the nonequilibrium behavior.