Asymptotic scaling in the two-dimensional $SU(3)$ $\sigma$-model at correlation length $4\times 10^5$

Abstract

We carry out a high-precision simulation of the two-dimensional $SU(3)$ principal chiral model at correlation lengths $\xi$ up to $\approx 4\times 10^5$, using a multi-grid Monte Carlo (MGMC) algorithm. 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. For $ξ\gtapprox 10^3$ we observe good asymptotic scaling in the bare coupling; at $\xi \approx 4\times 10^5$ the nonperturbative constant is within 2--3\% of its predicted limiting value.

13 pages (includes 3 figures), self-unpacking uuencoded .tar.gz

References in corpus (3)

• Multi-Grid Monte Carlo via $XY$ Embedding. II. Two-Dimensional $SU(3)$ Principal Chiral Model
• Reply to Comment on ``Asymptotic Scaling in the Two-Dimensional O(3) sigma-Model at Correlation Length 10^5"
• Dynamic Critical Behavior of Multi-Grid Monte Carlo for Two-Dimensional Nonlinear $\sigma$-Models

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