On the evaluation of universal non-perturbative constants in O(N) sigma models

We investigate the relation between on-shell and zero-momentum non-perturbative quantities entering the parametrization of the two-point Green function of two-dimensional non-linear O(N) sigma models. We present accurate estimates of ratios of mass scales and renormalization constants, obtained by an analysis of the strong-coupling expansion of the two-point Green function. These ratios allow to connect the exact on-shell results of Hasenfratz et al. [Phys. Lett. B 245 (1990) 522], Hasenfratz and Niedermayer [Phys. Lett. B 245 (1990) 529] and Balog and Niedermaier [hep-th/9612039] with typical zero-momentum lattice evaluations. Our results are supported by the 1/N-expansion. (C) 1997 Published by Elsevier Science B.V