Numerical study of the enlarged O(5) symmetry of the 3D antiferromagnetic RP2 spin model

We investigate by means of Monte Carlo simulation and finite-size scaling analysis the critical properties of the three-dimensional O(5) non-linear σ 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, provided 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 of the phase transitions are of the first order.