Testing Asymptotic Scaling and Nonabelian Symmetry Enhancement

TL;DR

This paper investigates the finite size scaling of correlation lengths in 2D O(3) and icosahedron spin models, finding evidence for a shared continuum limit and larger correlation lengths than earlier estimates.

Contribution

It provides new Monte Carlo data on finite size scaling and continuum limits, challenging previous estimates of correlation lengths in these models.

Findings

Models share the same continuum limit.

Scaling curve is above previous estimates.

Larger thermodynamic correlation lengths suggested.

Abstract

We determine some points on the finite size scaling curve for the correlation length in the two dimensional O(3) and icosahedron spin models. The Monte Carlo data are consistent with the two models possessing the same continuum limit. The data also suggest that the continuum scaling curve lies above the estimate of Kim and of Caracciolo et al and thus leads to larger thermodynamic values of of the correlation length than previously reported.