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Journal of Statistical Physics

, Volume 74, Issue 1–2, pp 313–348 | Cite as

Optimal multigrid algorithms for calculating thermodynamic limits

  • A. Brandt
  • M. Galun
  • D. Ron
Articles

Abstract

Beyond eliminating the critical slowing down, multigrid algorithms can also eliminate the need to produce many independent fine-grid configurations for averaging out their statistical deviations, by averaging over the many samples produced in coarse grids during the multigrid cycle. Thermodynamic limits can be calculated to accuracy ɛ in justO-2) computer operations. Examples described in detail and with results of numerical tests are the calculation of the susceptibility, the σ-susceptibility, and the average energy in Gaussian models, and also the determination of the susceptibility and the critical temperature in a two-dimensional Ising spin model. Extension to more advanced models is outlined.

Key Words

Multigrid Gaussian model Ising spin model XY model Monte Carlo thermodynamic limit coarsening by approximation 

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Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • A. Brandt
    • 1
  • M. Galun
    • 1
  • D. Ron
    • 1
  1. 1.Department of Applied Mathematics and Computer ScienceWeizmann Institute of ScienceRehovotIsrael

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