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Monte-Carlo Methods and Applications in Neutronics, Photonics and Statistical Physics pp 222–233Cite as

Monte Carlo sampling strategies for lattice gauge calculations

  • Statistical Physics
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Part of the book series: Lecture Notes in Physics ((LNP,volume 240))

Abstract

We have sought to optimize the elements of the Monte Carlo processes for thermalizing and decorrelating sequences of lattice gauge configurations and for this purpose, to develop computational and theoretical diagnostics to compare alternative techniques. These have been applied to speed up generations of random matrices, compare heat bath and Metropolis stepping methods, and to study autocorrelations of sequences in terms of the classical moment problem.

The efficient use of statistically correlated lattice data is an optimization problem depending on the relation between computer times to generate lattice sequences of sufficiently small correlation and times to analyze them. We can solve this problem with the aid of a representation of auto-correlation data for various step lags as moments of positive definite distributions, using methods known for the moment problem to put bounds on statistical variances, in place of estimating the variances by too-lengthy computer runs.

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References

  1. R S. Varga, “Matrix Iterative Analysis,” Chapter 2, Prentice Hall, Englewood Cliffs, NJ, 1962.

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  2. J. P. C. Kleijnen, “Statistical Techniques in Simulation,” Part II, Chapter V, Dekker, New York/Basel, 1975.

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  3. M. G. Krein and M. A. Rutman, “Linear Operators Leaving Invariant A Cone in a Banach Space,” Uspehi Nat. Nauk 3, (23) 3–95, English Translation: American Math. Soc., Translation 26.

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  4. M. Kendall and A. Stuart, “The Advanced Theory of Statistics, Volume 3, Chapter 48, Hafner Press, Macmillan, New York, 1976.

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  5. G. Guralnik, T. Warnock, and C. Zemach, “Factorization, Invariant Measure and Random Selection of Matrices in SU(n) and Other Groups,” and “Random Selection from Trace-Biased Invariant Distributions of SU(3) Matrices,” J. Comp. Phys., (to be published).

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Author information

Authors and Affiliations

  1. Los Alamos National Laboratory, 87545, Los Alamos, New Mexico, USA

    Gerald Guralnik & Charles Zemach

  2. Cray Research, Incorporated and Los Alamos National Laboratory, 87545, Los Alamos, New Mexico, USA

    Tony Warnock

Authors
  1. Gerald Guralnik
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  2. Charles Zemach
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  3. Tony Warnock
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Editor information

Raymond Alcouffe Robert Dautray Arthur Forster Guy Ledanois B. Mercier

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© 1985 Springer-Verlag

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Guralnik, G., Zemach, C., Warnock, T. (1985). Monte Carlo sampling strategies for lattice gauge calculations. In: Alcouffe, R., Dautray, R., Forster, A., Ledanois, G., Mercier, B. (eds) Monte-Carlo Methods and Applications in Neutronics, Photonics and Statistical Physics. Lecture Notes in Physics, vol 240. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0049051

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  • DOI: https://doi.org/10.1007/BFb0049051

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16070-0

  • Online ISBN: 978-3-540-39750-2

  • eBook Packages: Springer Book Archive

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