# UCL Discovery

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

Mana, G; Pelissetto, A; Sokal, AD; Multi-Grid Monte Carlo via $XY$ Embedding. II. Two-Dimensional $SU(3)$ Principal Chiral Model. Phys.Rev.D , 55 pp. 3674-3741. 10.1103/PhysRevD.55.3674.

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## 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 $z_{int,{\cal M}^2} \approx 0.45 \pm 0.02$ (subjective 68% confidence interval). Thus, for this asymptotically free model, critical slowing-down is greatly reduced compared to local algorithms, but not completely eliminated.

Type: Article Multi-Grid Monte Carlo via $XY$ Embedding. II. Two-Dimensional $SU(3)$ Principal Chiral Model 10.1103/PhysRevD.55.3674 http://dx.doi.org/10.1103/PhysRevD.55.3674 self-unpacking archive including .tex, .sty and .ps files; 126 pages including all figures hep-lat, hep-lat UCL > School of BEAMS > Faculty of Maths and Physical SciencesUCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics http://discovery.ucl.ac.uk/id/eprint/82847