Wolff-type embedding algorithms for general nonlinear σ-models

Sergio Caracciolo, Robert G. Edwards, Andrea Pelissetto, Alan D. Sokal

    Research output: Contribution to journalArticle

    Abstract

    We study a class of Monte Carlo algorithms for the nonlinear σ-model, based on A Wolff-type embedding of Ising spins into the target manifold M. We argue heuristically that, at least for an asymptotically free model, such an algorithm can have a dynamic critical exponent z « 2 only if the embedding is based on an (involutive) isometry of M whose fixed-point manifold has codimension 1. Such an isometry exist only if the manifold is a discrete quotient of a product of spheres. Numerical simulations of the idealized codimension-2 algorithm for the two-dimensional O(4)-symmetric σ-model yield zint,M2 = 1.5±0.5 (sujective 68% confidence interval), in agreement with our heuristic argument.

    Original languageEnglish (US)
    Pages (from-to)475-541
    Number of pages67
    JournalNuclear Physics, Section B
    Volume403
    Issue number1-2
    DOIs
    StatePublished - Aug 16 1993

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    ASJC Scopus subject areas

    • Nuclear and High Energy Physics

    Cite this

    Caracciolo, S., Edwards, R. G., Pelissetto, A., & Sokal, A. D. (1993). Wolff-type embedding algorithms for general nonlinear σ-models. Nuclear Physics, Section B, 403(1-2), 475-541. https://doi.org/10.1016/0550-3213(93)90044-P

    Wolff-type embedding algorithms for general nonlinear σ-models. / Caracciolo, Sergio; Edwards, Robert G.; Pelissetto, Andrea; Sokal, Alan D.

    In: Nuclear Physics, Section B, Vol. 403, No. 1-2, 16.08.1993, p. 475-541.

    Research output: Contribution to journalArticle

    Caracciolo, S, Edwards, RG, Pelissetto, A & Sokal, AD 1993, 'Wolff-type embedding algorithms for general nonlinear σ-models', Nuclear Physics, Section B, vol. 403, no. 1-2, pp. 475-541. https://doi.org/10.1016/0550-3213(93)90044-P
    Caracciolo, Sergio ; Edwards, Robert G. ; Pelissetto, Andrea ; Sokal, Alan D. / Wolff-type embedding algorithms for general nonlinear σ-models. In: Nuclear Physics, Section B. 1993 ; Vol. 403, No. 1-2. pp. 475-541.
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