Generalized Wolff-type embedding algorithms for 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 such an algorithm can have 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 exists only if the manifold is a product of spheres and discrete quotients of spheres. Numerical simulations of the codimension-2 algorithm for the two-dimensional O(4)-symmetric σ-model yield z = 1.5 ± 0.3, in agreement with our heuristic argument.

    Original languageEnglish (US)
    Pages (from-to)72-75
    Number of pages4
    JournalNuclear Physics B - Proceedings Supplements
    Volume20
    Issue numberC
    DOIs
    StatePublished - May 20 1991

    Fingerprint

    embedding
    quotients
    exponents
    products
    simulation

    ASJC Scopus subject areas

    • Nuclear and High Energy Physics

    Cite this

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

    In: Nuclear Physics B - Proceedings Supplements, Vol. 20, No. C, 20.05.1991, p. 72-75.

    Research output: Contribution to journalArticle

    Caracciolo, Sergio ; Edwards, Robert G. ; Pelissetto, Andrea ; Sokal, Alan D. / Generalized Wolff-type embedding algorithms for nonlinear σ-models. In: Nuclear Physics B - Proceedings Supplements. 1991 ; Vol. 20, No. C. pp. 72-75.
    @article{d0ff2d8399b64868b1bfae9dcaee7bf6,
    title = "Generalized Wolff-type embedding algorithms for nonlinear σ-models",
    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 such an algorithm can have 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 exists only if the manifold is a product of spheres and discrete quotients of spheres. Numerical simulations of the codimension-2 algorithm for the two-dimensional O(4)-symmetric σ-model yield z = 1.5 ± 0.3, in agreement with our heuristic argument.",
    author = "Sergio Caracciolo and Edwards, {Robert G.} and Andrea Pelissetto and Sokal, {Alan D.}",
    year = "1991",
    month = "5",
    day = "20",
    doi = "10.1016/0920-5632(91)90883-G",
    language = "English (US)",
    volume = "20",
    pages = "72--75",
    journal = "Nuclear and Particle Physics Proceedings",
    issn = "2405-6014",
    publisher = "Elsevier",
    number = "C",

    }

    TY - JOUR

    T1 - Generalized Wolff-type embedding algorithms for nonlinear σ-models

    AU - Caracciolo, Sergio

    AU - Edwards, Robert G.

    AU - Pelissetto, Andrea

    AU - Sokal, Alan D.

    PY - 1991/5/20

    Y1 - 1991/5/20

    N2 - 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 such an algorithm can have 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 exists only if the manifold is a product of spheres and discrete quotients of spheres. Numerical simulations of the codimension-2 algorithm for the two-dimensional O(4)-symmetric σ-model yield z = 1.5 ± 0.3, in agreement with our heuristic argument.

    AB - 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 such an algorithm can have 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 exists only if the manifold is a product of spheres and discrete quotients of spheres. Numerical simulations of the codimension-2 algorithm for the two-dimensional O(4)-symmetric σ-model yield z = 1.5 ± 0.3, in agreement with our heuristic argument.

    UR - http://www.scopus.com/inward/record.url?scp=4243881248&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=4243881248&partnerID=8YFLogxK

    U2 - 10.1016/0920-5632(91)90883-G

    DO - 10.1016/0920-5632(91)90883-G

    M3 - Article

    VL - 20

    SP - 72

    EP - 75

    JO - Nuclear and Particle Physics Proceedings

    JF - Nuclear and Particle Physics Proceedings

    SN - 2405-6014

    IS - C

    ER -