Wolff-type embedding algorithms for general nonlinear σ-models

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

    Research output: Contribution to journalArticlepeer-review

    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

    ASJC Scopus subject areas

    • Nuclear and High Energy Physics

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