Comment on `Asymptotic Scaling in the Two-Dimensional O(3) sigma-Model at Correlation Length 10^5' by S. Caracciolo et al

TL;DR

This paper critiques the reliance on small lattice extrapolations for determining nonperturbative quantities in the 2D O(3) sigma-model, emphasizing the need for larger-scale or nonperturbative methods.

Contribution

It provides a critical analysis of previous extrapolation methods, arguing they are insufficient for accurate nonperturbative quantity determination.

Findings

Small lattice extrapolations are inadequate for nonperturbative predictions

Perturbative information alone cannot reliably determine correlation lengths

Highlights the importance of nonperturbative approaches

Abstract

We explain why in our view an extrapolation from small lattices containing only perturbative information cannot be sufficient to determine nonperturbative qunatities and therefore cannot lead to a trustworthy determination of the correlation length.