ASYMPTOTIC SCALING IN THE 2-DIMENSIONAL SU(3) SIGMA-MODEL AT CORRELATION LENGTH 4X10(5)

We carry out a high-precision simulation of the two-dimensional SU(3) principal chiral model at correlation lengths xi up to approximate to 4x10(5), using a multigrid Monte Carlo (MGMC) algorithm. We extrapolat e the finite-volume Monte Carlo data to infinite volume using finite-s ize-scaling theory, and we discuss carefully the systematic and statis tical errors in this extrapolation. We then compare the extrapolated d ata to the renormalization-group predictions. For xi greater than or e qual to 10(3) we observe good asymptotic scaling in the hare coupling; at xi approximate to 4X10(5) the nonperturbative constant is within 2 -3% of its predicted limiting value.