# UCL Discovery

## Asymptotic scaling in the two-dimensional $SU(3)$ $σ$-model at correlation length $4 \times 10^5$

Mana, G; Pelissetto, A; Sokal, AD; (1996) Asymptotic scaling in the two-dimensional $SU(3)$ $σ$-model at correlation length $4 \times 10^5$. Phys.Rev.D , 54 1252 - 1255. 10.1103/PhysRevD.54.R1252.

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## Abstract

We carry out a high-precision simulation of the two-dimensional $SU(3)$ principal chiral model at correlation lengths $\xi$ up to $\approx\! 4 \times 10^5$, using a multi-grid Monte Carlo (MGMC) algorithm. 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. For $\xi \gtapprox 10^3$ we observe good asymptotic scaling in the bare coupling; at $\xi \approx 4 \times 10^5$ the nonperturbative constant is within 2--3\% of its predicted limiting value.

Type: Article Asymptotic scaling in the two-dimensional $SU(3)$ $σ$-model at correlation length $4 \times 10^5$ 10.1103/PhysRevD.54.R1252 http://dx.doi.org/10.1103/PhysRevD.54.R1252 13 pages (includes 3 figures), self-unpacking uuencoded .tar.gz hep-lat, hep-lat UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics

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