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Systematic errors due to linear congruential random-number generators with the Swendsen-Wang algorithm: a warning.

Giovanni Ossola1, Alan D Sokal

  • 1Department of Physics, New York University, 4 Washington Place, New York, New York 10003, USA. giovanni.ossola@physics.nyu.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2004
PubMed
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Linear congruential pseudo-random number generators can introduce errors in Monte Carlo simulations with the Swendsen-Wang algorithm. Randomizing bond updates or using large-modulus generators mitigates these systematic errors.

Area of Science:

  • Computational physics
  • Statistical mechanics

Background:

  • Monte Carlo simulations are crucial for studying complex systems.
  • The Swendsen-Wang algorithm is a widely used Markov chain Monte Carlo method for Ising models.
  • Pseudo-random number generators (PRNGs) are fundamental to simulation accuracy.

Purpose of the Study:

  • To investigate systematic errors in Monte Carlo simulations caused by linear congruential PRNGs.
  • To identify the conditions under which these errors occur in the Swendsen-Wang algorithm.
  • To propose methods for mitigating these simulation artifacts.

Main Methods:

  • Analysis of linear congruential pseudo-random number generators.
  • Application of the Swendsen-Wang algorithm to lattice simulations.
  • Identification of correlations within bond-update sweeps.

Related Experiment Videos

  • Testing strategies for error reduction, including random and aperiodic updates.

    • Main Results:

    • Linear congruential PRNGs can induce systematic errors when lattice size is a multiple of a large power of 2 and one random number is used per bond.
    • These errors stem from correlations within a single bond-update half-sweep.
    • Errors are significantly reduced by randomizing bond update order or using an aperiodic update strategy.
    • Employing PRNGs with a large modulus (≥60 bits) also diminishes these systematic errors.

    Conclusions:

    • The choice of pseudo-random number generator and update strategy critically impacts the accuracy of Monte Carlo simulations.
    • Careful selection of PRNGs and implementation of randomized or aperiodic update schemes are essential for reliable Swendsen-Wang simulations.
    • Understanding and addressing PRNG-induced correlations is vital for robust computational physics research.