Dynamic critical behavior of multi-grid Monte Carlo for two-dimensional nonlinear σ-models

Gustavo Mana, Tereza Mendes, Andrea Pelissetto, Alan D. Sokal

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We introduce a new and very convenient approach to multi-grid Monte Carlo (MGMC) algorithms for general nonlinear σ-models: it is based on embedding an XY model into the given σ-model, and then updating the induced XY model using a standard XY-model MGMC code. We study the dynamic critical behavior of this algorithm for the two-dimensional O(N) σ-models with N = 3,4,8 and for the SU(3) principal chiral model. We find that the dynamic critical exponent z varies systematically between these different asymptotically free models: it is approximately 0.70 for O(3), 0.60 for O(4), 0.50 for O(8), and 0.45 for SU(3). It goes without saying that we have no theoretical explanation of this behavior.

    Original languageEnglish (US)
    Pages (from-to)796-799
    Number of pages4
    JournalNuclear Physics B - Proceedings Supplements
    Volume47
    Issue number1-3
    DOIs
    StatePublished - Mar 1996

    ASJC Scopus subject areas

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

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