O(N) AND RP(N-1) MODELS IN 2 DIMENSIONS

I provide evidence that the 2D RP(N-1) model for N greater than or equ al to 3 is equivalent to the O(N)-invariant nonlinear sigma model in t he continuum limit. To this end, I mainly study particular versions of the models, to be called constraint models. I prove that the constrai nt RP(N-1) and O(N) models are equivalent for sufficiently weak coupli ng. Numerical results for the step-scaling function of the running cou pling 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 st andard action. I show that in the weak coupling limit periodic boundar y conditions for the RP(N-1) model correspond to fluctuating boundary conditions for the O(N) model. The effect of boundary conditions on fi nite size scaling curves is discussed. It is concluded, in contrast wi th Caracciolo et al., that RP(N-1) and O(N) models share a unique univ ersality class.