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High precision simulations with fast algorithms

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Computational Methods in Field Theory

Part of the book series: Lecture Notes in Physics ((LNP,volume 409))

Abstract

A brief non-rigorous introduction to the Monte Carlo method for the simulation of lattice quantum field theoretical models is given. The associated problem of critical slowing down in the continuum limit is addressed together with its partial solution for some classes of systems. The version of overrelaxation mostly used in practice, with alternating microcanonical and standard updates, is analyzed exactly for free fields and described in numerical applications to spin and gauge systems. Cluster algorithms are briefly introduced, and applications to the two dimensional O(3) δ-model are described in some detail. They include the exploration of scaling behavior, a numerical estimate of scattering phases and the demonstration and test of a general technique to compute running renormalized coupling constants in asymptotically free theories. We conclude with remarks on the present status of algorithm development.

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Authors and Affiliations

  1. Theory Division, CERN, CH-1211, Genéve 23, Switzerland

    Ulli Wolff

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  1. Ulli Wolff
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H. Gausterer C. B. Lang

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© 1992 Springer-Verlag

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Wolff, U. (1992). High precision simulations with fast algorithms. In: Gausterer, H., Lang, C.B. (eds) Computational Methods in Field Theory. Lecture Notes in Physics, vol 409. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55997-3_32

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  • DOI: https://doi.org/10.1007/3-540-55997-3_32

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55997-9

  • Online ISBN: 978-3-540-47338-1

  • eBook Packages: Springer Book Archive

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