Comparison between Theoretical Four-Loop Predictions and Monte Carlo Calculations in the Two-Dimensional $N$-Vector Model for $N=3,4,8$

Abstract

We have computed the four-loop contribution to the beta-function and to the anomalous dimension of the field for the two-dimensional lattice $N$-vector model. This allows the determination of the second perturbative correction to various long-distance quantities like the correlation lengths and the susceptibilities. We compare these predictions with new Monte Carlo data for $N=3,4,8$. From these data we also extract the values of various universal nonperturbative constants, which we compare with the predictions of the $1/N$ expansion.

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References in corpus (1)

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

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