Multi-Grid Monte Carlo via $XY$ Embedding. II. Two-Dimensional $SU(3)$ Principal Chiral Model

Abstract

We carry out a high-precision simulation of the two-dimensional $SU(3)$ principal chiral model at correlation lengths $\xi$ up to $\sim 4\times 10^5$, using a multi-grid 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 $\approx 12$ at $\xi \sim 25$, decreases to $\approx 2$ at $\xi \sim 4\times 10^5$. We also analyze the dynamic critical behavior of the MGMC algorithm using lattices up to $256\times 256$, finding the dynamic critical exponent $z_{int,{\mathcal{M}}^2}\approx 0.45\pm 0.02$ (subjective 68% confidence interval). Thus, for this asymptotically free model, critical slowing-down is greatly reduced compared to local algorithms, but not completely eliminated.

self-unpacking archive including .tex, .sty and .ps files; 126 pages including all figures

References in corpus (6)

• Asymptotic scaling in the two-dimensional $SU(3)$ $\sigma$-model at correlation length $4\times 10^5$
• Improved lattice actions
• Multi-Grid Monte Carlo via $XY$ Embedding I. General Theory and Two-Dimensional $O(N)$-Symmetric Nonlinear $\sigma$-Models
• Nonperturbative Renormalon Structure of Infrared Unstable Theories
• Reply to Comment on ``Asymptotic Scaling in the Two-Dimensional O(3) sigma-Model at Correlation Length 10^5"
• QCD $\beta$ Function with Two Flavors of Dynamical Wilson Fermions

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