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Multigrid Methods III pp 61–82Cite as

Birkhäuser

Multiscale Monte Carlo Algorithms in Statistical Mechanics and Quantum Field Theory

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Abstract

Conventional Monte Carlo simulation algorithms for models in statistical mechanics and quantum field theory are afflicted by problems caused by their locality. They become highly inefficient if investigations of critical or nearly-critical systems, i.e., systems with important large scale phenomena, are undertaken. We present two types of multiscale approaches that alleveate problems of this kind: stochastic cluster algorithms and multigrid Monte Carlo simulation algorithms. Another formidable computational problem in simulations of phenomenologically relevant field theories with fermions is the need for frequently inverting the Dirac operator. This inversion can be accelerated considerably by means of deterministic multigrid methods, very similar to the ones used for the numerical solution of differential equations.

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Author information

Authors and Affiliations

  1. Physikalisches Institut, Universität Bonn, Nußallee 12, 5300, Bonn 1, Federal Republic of Germany

    P. G. Lauwers

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  1. P. G. Lauwers
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Editor information

Editors and Affiliations

  1. Institut für Informatik und Praktische Mathematik, Universität Kiel, Olshausenstrasse 40, D-2300, Kiel 1, Germany

    W. Hackbusch

  2. Gesellschaft für Mathematik und Datenverarbeitung mbH, Postfach 1240, Schloss Birlinghoven, D-5205, Sankt Augustin 1, Germany

    U. Trottenberg

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© 1991 Springer Basel AG

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Lauwers, P.G. (1991). Multiscale Monte Carlo Algorithms in Statistical Mechanics and Quantum Field Theory. In: Hackbusch, W., Trottenberg, U. (eds) Multigrid Methods III. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 98. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5712-3_4

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  • DOI: https://doi.org/10.1007/978-3-0348-5712-3_4

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5714-7

  • Online ISBN: 978-3-0348-5712-3

  • eBook Packages: Springer Book Archive

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