0 v 1 1 J ul 1 99 7 Comment on “ Scaling Hypothesis for the Spectral Densities in the O ( 3 ) Nonlinear Sigma Model ”

We comment on the recent paper by Balog and Niedermaier [1]. Balog and Niedermaier’s scaling hypothesis for the spectral densities in the O(3) nonlinear σ model [1] does not seem to be supported by the Monte Carlo data. As we showed in a recent paper [2], the numerics indicate that the continuum limit of the lattice O(3) σ model agrees as well with the S-matrix prediction [3] as with the continuum limit of the dodecahedron spin model. In the latter model the massive high temperature phase must terminate at some finite inverse temperature β. It is well known that asymptotic freedom requires the current 2-point function to diverge for p/m→∞ [4]. However in another recent paper we proved that the current 2-point function is bounded at finite β, due to reflection positivity and a Ward identity. Consequently, unless the observed agreement between the O(3) and dodecahedron spin model is accidental and disappears at larger values of p/m,