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

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 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 $\xi \sim 10^5$.

3 pages including 3 figures, 170894 bytes Postscript, contribution to Lattice '94; see also hep-lat/9409004 and hep-lat/9411009

References in corpus (1)

• Lattice Perturbation Theory for $O(N)$-Symmetric $\sigma$-Models with General Nearest-Neighbour Action I. Conventional Perturbation Theory

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