Parallelization of the Wolff Single-Cluster Algorithm

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Kaupužs, Jevgenijs; Rimšāns, Jānis; Melnik, Roderick V.N.
Applied Mathematics; Mathematics
article description
A parallel [open multiprocessing (OpenMP)] implementation of the Wolff single-cluster algorithm has been developed and tested for the three-dimensional (3D) Ising model. The developed procedure is generalizable to other lattice spin models and its effectiveness depends on the specific application at hand. The applicability of the developed methodology is discussed in the context of the applications, where a sophisticated shuffling scheme is used to generate pseudorandom numbers of high quality, and an iterative method is applied to find the critical temperature of the 3D Ising model with a great accuracy. For the lattice with linear size L=1024, we have reached the speedup about 1.79 times on two processors and about 2.67 times on four processors, as compared to the serial code. According to our estimation, the speedup about three times on four processors is reachable for the O(n) models with n ≥ 2. Furthermore, the application of the developed OpenMP code allows us to simulate larger lattices due to greater operative (shared) memory available.