ar X iv : h ep - l at / 9 50 70 08 v 1 7 J ul 1 99 5 DAMTP 95 - 40 O ( N ) and RP N − 1 Models in Two Dimensions

I provide evidence that the 2D RP N −1 model for N ≥ 3 is equivalent to the O(N)-invariant non-linear σ-model in the continuum limit. To this end, I mainly study particular versions of the models, to be called constraint models. I prove that the constraint RP N −1 and O(N) models are equivalent for sufficiently weak coupling. Numerical results for the step-scaling function of the running coupling ¯ g 2 = m(L)L are presented. The data confirm that the constraint O(N) model is in the same universality class as the O(N) model with standard action. I show that the differences in the finite size scaling curves of RP N −1 and O(N) models observed by Caracciolo et al. can be explained as a boundary effect. It is concluded, in contrast to Caracciolo et al., that RP N −1 and O(N) models share a unique universality class.