Multigrid Monte Carlo simulation via [Formula presented] embedding. II. Two-dimensional SU(3) principal chiral model

Gustavo Mana, Andrea Pelissetto, Alan D. Sokal

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We carry out a high-precision simulation of the two-dimensional SU(3) principal chiral model at correlation lengths ξ up to [Formula presented], using a multigrid Monte Carlo (MGMC) algorithm and approximately one year of Cray C-90 CPU time. We extrapolate the finite-volume Monte Carlo data to infinite volume using finite-size-scaling theory, and we discuss carefully the systematic and statistical errors in this extrapolation. We then compare the extrapolated data to the renormalization-group predictions. The deviation from asymptotic scaling, which is ≈12% at ξ∼25, decreases to ≈2% at [Formula presented]. We also analyze the dynamic critical behavior of the MGMC algorithm using lattices up to 256×256, finding the dynamic critical exponent [Formula presented] (subjective 68% confidence interval). Thus, for this asymptotically free model, critical slowing-down is greatly reduced compared to local algorithms, but not completely eliminated.

    Original languageEnglish (US)
    Pages (from-to)3674-3741
    Number of pages68
    JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
    Volume55
    Issue number6
    DOIs
    StatePublished - 1997

    ASJC Scopus subject areas

    • Nuclear and High Energy Physics
    • Physics and Astronomy (miscellaneous)

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