We carry out a high-precision simulation of the two-dimensional SU(3) principal chiral model at correlation lengths ξ up to [Formula presented], using a multigrid 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 ≈12% at ξ∼25, decreases to ≈2% at [Formula presented]. We also analyze the dynamic critical behavior of the MGMC algorithm using lattices up to 256×256, finding the dynamic critical exponent [Formula presented] (subjective 68% confidence interval). Thus, for this asymptotically free model, critical slowing-down is greatly reduced compared to local algorithms, but not completely eliminated.
|Original language||English (US)|
|Number of pages||68|
|Journal||Physical Review D - Particles, Fields, Gravitation and Cosmology|
|State||Published - 1997|
ASJC Scopus subject areas
- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)