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Efficient parallelization of the 2D Swendsen-Wang algorithm

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  • Hackl, R.
  • Matuttis, H.-G.
  • Singer, J.M.
  • Husslein, Th.
  • Morgenstern, I.

Abstract

We established a fast Swendsen-Wang algorithm for the two-dimensional Ising model on parallel computers with a high efficiency. On an Intel paragon with 140 processors we reached spin update times of only 14 ns with an efficiency of 89%. This algorithm was used to examine the non-equilibrium relaxation of magnetization and energy in large Ising systems of a size up to 17920 × 17920 spins. Nevertheless we observed still a strong finite-size effect for the magnetization. We assume both magnetization and energy decay to behave like (t + Δ)-λe-bt in an infinitely large system. Thus, for long times magnetization and energy show an exponential, asymtotic time-dependence, implying a critical dynamic exponent z of zero.

Suggested Citation

  • Hackl, R. & Matuttis, H.-G. & Singer, J.M. & Husslein, Th. & Morgenstern, I., 1994. "Efficient parallelization of the 2D Swendsen-Wang algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 212(3), pages 261-276.
    • Handle: RePEc:eee:phsmap:v:212:y:1994:i:3:p:261-276
    DOI: 10.1016/0378-4371(94)90332-8
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    References listed on IDEAS

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    1. Siegert, Markus & Stauffer, Dietrich, 1994. "Energy relaxation in Ising models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 208(1), pages 31-34.
    2. Tamayo, Pablo, 1993. "Magnetization relaxation to equilibrium on large 2D Swendsen-Wang Ising models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 201(4), pages 543-546.
    3. Mike Flanigan & Pablo Tamayo, 1992. "A Parallel Cluster Labeling Method For Monte Carlo Dynamics," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 3(06), pages 1235-1249.
    4. J. Kertész & D. Stauffer, 1992. "Swendsen-Wang Dynamics On Large 2d Critical Ising Models," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 3(06), pages 1275-1279.
    5. Ito, Nobuyasu & Kohring, Gregory A., 1993. "Non-equilibrium critical relaxation of the Wolff dynamics of the Ising model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 201(4), pages 547-556.
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    Cited by:

    1. Flanigan, M. & Tamayo, P., 1995. "Parallel cluster labeling for large-scale Monte Carlo simulations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 215(4), pages 461-480.

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