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

Gustavo Mana·Andrea Pelissetto·Alan D. Sokal
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Abstract

We carry out a high-precision simulation of the two-dimensional $SU(3)$ principal chiral model at correlation lengths $ξ$ 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 $ξ\gtapprox 10^3$ we observe good asymptotic scaling in the bare coupling; at $ξ\approx 4 \times 10^5$ the nonperturbative constant is within 2--3\% of its predicted limiting value.

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Gustavo Mana, Andrea Pelissetto, Alan D. Sokal. 1996-02-13. Asymptotic scaling in the two-dimensional $SU(3)$ $σ$-model at correlation length $4 \times 10^5$. https://doi.org/10.1103/physrevd.54.r1252

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