Multigrid Monte Carlo simulation via XY embedding. II. Two-dimensional SU(3) principal chiral model

Journal Article · Sat Mar 01 00:00:00 EST 1997 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.55.3674· OSTI ID:517016

Mana, G ^[1]; Pelissetto, A ^[2]; Sokal, A D ^[1]

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1. Department of Physics, New York University, 4 Washington Place, New York, New York 10003 (United States)
2. Dipartimento di Fisica, Universita degli Studi di Pisa, Pisa 56100 (Italy)

We carry out a high-precision simulation of the two-dimensional SU(3) principal chiral model at correlation lengths {xi} up to {approximately}4{times}10{sup 5}, 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 {approx}12{percent} at {xi}{approximately}25, decreases to {approx}2{percent} at {xi}{approximately}4{times}10{sup 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{sub int,M{sup 2}}{approx}0.45{plus_minus}0.02 (subjective 68{percent} confidence interval). Thus, for this asymptotically free model, critical slowing-down is greatly reduced compared to local algorithms, but not completely eliminated. {copyright} {ital 1997} {ital The American Physical Society}

• OSTI ID: 517016
• Journal Information: Physical Review, D, Vol. 55, Issue 6; Other Information: PBD: Mar 1997
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
QUANTUM FIELD THEORY
CHIRAL SYMMETRY
SIMULATION
DIFFERENTIAL EQUATIONS
SU-3 GROUPS
MONTE CARLO METHOD
SCALING
RENORMALIZATION
CRITICALITY
ALGORITHMS
ASYMPTOTIC SOLUTIONS
ERRORS
CORRELATIONS
TWO-DIMENSIONAL CALCULATIONS