Generalized Wolff-type embedding algorithms for nonlinear σ-models

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

    Research output: Contribution to journalArticlepeer-review


    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)
    Issue numberC
    StatePublished - May 20 1991

    ASJC Scopus subject areas

    • Atomic and Molecular Physics, and Optics
    • Nuclear and High Energy Physics


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