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We carry out a high-precision simulation of the two-dimensional $SU(3)$principal chiral model at correlation lengths $\xi$ up to $\approx\! 4 \times10^5$, using a multi-grid Monte Carlo (MGMC) algorithm. We extrapolate thefinite-volume Monte Carlo data to infinite volume using finite-size-scalingtheory, and we discuss carefully the systematic and statistical errors in thisextrapolation. We then compare the extrapolated data to therenormalization-group predictions. For $\xi \gtapprox 10^3$ we observe goodasymptotic scaling in the bare coupling; at $\xi \approx 4 \times 10^5$ thenonperturbative constant is within 2--3\% of its predicted limiting value.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Asymptotic scaling in the two-dimensional SU(3)<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>σ</mml:mi></mml:math>model at correlation length 4 ×<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mn>10</mml:mn></mml:mrow><mml:mrow><mml:mn>5</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>

Asymptotic scaling in the two-dimensional SU(3)σmodel at correlation length 4 ×105