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

Sergio Caracciolo; Robert G. Edwards; Andrea Pelissetto; Alan D. Sokal

doi:10.1103/PhysRevLett.75.1891

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

High Energy Physics - Lattice 2009-10-22 v2

Authors: Sergio Caracciolo , Robert G. Edwards , Andrea Pelissetto , Alan D. Sokal

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Abstract

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 $\xi \sim 10^5$ .

Keywords

o(3) sigma-model asymptotic scaling monte carlo simulation finite-size scaling correlation length

Cite

@article{arxiv.hep-lat/9411009,
  title  = {Asymptotic Scaling in the Two-Dimensional $O(3)$ $\sigma$-Model at Correlation Length $10^5$},
  author = {Sergio Caracciolo and Robert G. Edwards and Andrea Pelissetto and Alan D. Sokal},
  journal= {arXiv preprint arXiv:hep-lat/9411009},
  year   = {2009}
}

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

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

Abstract

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