### Abstract

We carry out a high-precision simulation of the two-dimensional SU(3) principal chiral model at correlation lengths ξ up to ∼4×10^{;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 ≈12% at ξ∼25, decreases to ≈2% at ξ∼4×10^{;5};. We also analyze the dynamic critical behavior of the MGMC algorithm using lattices up to 256×256, finding the dynamic critical exponent z^{int,M2};≈0.45±0.02 (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) |
---|---|

Pages (from-to) | 3674-3741 |

Number of pages | 68 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 55 |

Issue number | 6 |

State | Published - Mar 15 1997 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*55*(6), 3674-3741.

**Multigrid Monte Carlo simulation via XY embedding. II. Two-dimensional SU(3) principal chiral model.** / Mana, Gustavo; Pelissetto, Andrea; Sokal, Alan D.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 55, no. 6, pp. 3674-3741.

}

TY - JOUR

T1 - Multigrid Monte Carlo simulation via XY embedding. II. Two-dimensional SU(3) principal chiral model

AU - Mana, Gustavo

AU - Pelissetto, Andrea

AU - Sokal, Alan D.

PY - 1997/3/15

Y1 - 1997/3/15

N2 - We carry out a high-precision simulation of the two-dimensional SU(3) principal chiral model at correlation lengths ξ up to ∼4×10;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 ≈12% at ξ∼25, decreases to ≈2% at ξ∼4×10;5;. We also analyze the dynamic critical behavior of the MGMC algorithm using lattices up to 256×256, finding the dynamic critical exponent zint,M2;≈0.45±0.02 (subjective 68% confidence interval). Thus, for this asymptotically free model, critical slowing-down is greatly reduced compared to local algorithms, but not completely eliminated.

AB - We carry out a high-precision simulation of the two-dimensional SU(3) principal chiral model at correlation lengths ξ up to ∼4×10;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 ≈12% at ξ∼25, decreases to ≈2% at ξ∼4×10;5;. We also analyze the dynamic critical behavior of the MGMC algorithm using lattices up to 256×256, finding the dynamic critical exponent zint,M2;≈0.45±0.02 (subjective 68% confidence interval). Thus, for this asymptotically free model, critical slowing-down is greatly reduced compared to local algorithms, but not completely eliminated.

UR - http://www.scopus.com/inward/record.url?scp=0000458159&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000458159&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0000458159

VL - 55

SP - 3674

EP - 3741

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 6

ER -