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arXiv · hep-lat/9411064

Two-Dimensional $O(3)$ $σ$-Model up to Correlation Length $10^5$

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 $σ$-model at correlation lengths $ξ$ 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 compare the extrapolated data to the renormalization-group predictions. The deviation from asymptotic scaling, which is $\approx 25\%$ at $ξ\sim 10^2$, decreases to $\approx 4\%$ at $ξ\sim 10^5$.

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Sergio Caracciolo, Robert G. Edwards, Andrea Pelissetto, Alan D. Sokal. 1994-11-28. Two-Dimensional $O(3)$ $σ$-Model up to Correlation Length $10^5$. https://doi.org/10.1016/0920-5632(95)00371-f

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