Multigrid Monte Carlo simulation via XY embedding. II. Two-dimensional SU(3) principal chiral model

Gustavo Mana, Andrea Pelissetto, Alan D. Sokal

    Research output: Contribution to journalArticle

    Abstract

    We carry out a high-precision simulation of the two-dimensional SU(3) principal chiral model at correlation lengths ξ up to ∼4×10;5;, 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 ξ∼4×10;5;. We also analyze the dynamic critical behavior of the MGMC algorithm using lattices up to 256×256, finding the dynamic critical exponent zint,M2;≈0.45±0.02 (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
    StatePublished - Mar 15 1997

    Fingerprint

    Monte Carlo Algorithm
    embedding
    Monte Carlo Simulation
    Critical Slowing down
    Scaling Theory
    Local Algorithms
    Extrapolate
    Finite-size Scaling
    Correlation Length
    CPU Time
    Critical Behavior
    Extrapolation
    Finite Volume
    Renormalization Group
    Critical Exponents
    Dynamic Behavior
    Confidence interval
    scaling
    Deviation
    simulation

    ASJC Scopus subject areas

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

    Cite this

    Multigrid Monte Carlo simulation via XY embedding. II. Two-dimensional SU(3) principal chiral model. / Mana, Gustavo; Pelissetto, Andrea; Sokal, Alan D.

    In: Physical Review D - Particles, Fields, Gravitation and Cosmology, Vol. 55, No. 6, 15.03.1997, p. 3674-3741.

    Research output: Contribution to journalArticle

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