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We present the GPU calculation with the common unified device architecture(CUDA) for the Swendsen-Wang multi-cluster algorithm of two-dimensionalclassical spin systems. We adjust the two connected component labelingalgorithms recently proposed with CUDA for the assignment of the cluster in theSwendsen-Wang algorithm. Starting with the q-state Potts model, we extend ourimplementation to the system of vector spins, the q-state clock model, with theidea of embedded cluster. We test the performance, and the calculation time onGTX580 is obtained as 2.51 nano sec per a spin flip for the q=2 Potts model(Ising model) and 2.42 nano sec per a spin flip for the q=6 clock model withthe linear size L=4096 at the critical temperature, respectively. Thecomputational speed for the q=2 Potts model on GTX580 is 12.4 times as fast asthe calculation speed on a current CPU core. That for the q=6 clock model onGTX580 is 35.6 times as fast as the calculation speed on a current CPU core.

GPU-based Swendsen-Wang multi-cluster algorithm for the simulation of two-dimensional classical spin systems