Asymptotic Scaling in the Two-Dimensional $O(3)$ $σ$-Model at Correlation Length $10^5$

Details Asymptotic Scaling in the Two-Dimensional $O(3)$ $σ$-Model at Correlation Length $10^5$ Asymptotic Scaling in the Two-Dimensional $O(3)$ $σ$-Model at Correlation Length $10^5$

1994-11-07

arxiv.org/abs/hep-lat/9411009v2

Phys.Rev.Lett. 75 (1995) 1891-1894

Physics

High Energy Physics

High Energy Physics - Lattice

11 pages including 3 figures, 278964 bytes Postscript (changed storage format)

Scientific paper

10.1103/PhysRevLett.75.1891

We carry out a high-precision Monte Carlo simulation of the two-dimensional $O(3)$-invariant $\sigma$-model at correlation lengths $\xi$ up to $\sim 10^5$. Our work employs a new and powerful method for extrapolating finite-volume Monte Carlo data to infinite volume, based on finite-size-scaling theory. 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 $\approx 25\%$ at $\xi \sim 10^2$, decreases to $\approx 4\%$ at $\xi \sim 10^5$.

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