  We investigate by means of Monte Carlo simulation and Finite-Size Scaling
analysis the critical properties of the three dimensional O(5) non linear sigma
model and of the antiferromagnetic RP2 model, both of them regularized on a
lattice. High accuracy estimates are obtained for the critical exponents,
universal dimensionless quantities and critical couplings. It is concluded that
both models belong to the same Universality Class, provide that rather non
standard identifications are made for the momentum-space propagator of the RP2
model. We have also investigated the phase diagram of the RP2 model extended by
a second-neighbor interaction. A rich phase diagram is found, where most phase
transitions are first order.
