Testing Asymptotic Scaling and Nonabelian Symmetry Enhancement

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 [1] and Caracciolo et al [2] and thus leads to larger thermodynamic values of of the correlation length than previously reported. In 1993 Kim [1] proposed using finite size scaling to obtain the thermodynamic value of the correlation length ξ in the two dimensional (2D) nonlinear σ model at given inverse temperature β. He claimed that he could predict correctly (less than 2% error) values as large as 15000 from measurements taken on lattices not larger than 283× 283. Kim’s method was adopted by Caracciolo et al [2], who, after refining it and collecting data at a 180 pairs of L and β values claimed to have such control over the scaling curve that they