TY - JOUR

T1 - Multigrid Monte Carlo simulation via [Formula presented] embedding. II. Two-dimensional SU(3) principal chiral model

AU - Mana, Gustavo

AU - Pelissetto, Andrea

AU - Sokal, Alan D.

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevD.55.3674

DO - 10.1103/PhysRevD.55.3674

M3 - Article

AN - SCOPUS:0000458159

SN - 1550-7998

VL - 55

SP - 3674

EP - 3741

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

IS - 6

ER -