Asymptotic low-temperature behavior of two-dimensional RPN-1 models

We investigate the low-temperature behavior of two-dimensional (2D) RPN-1 models, characterized by a global O(N) symmetry and a local Z2 symmetry. For N=3 we perform large-scale simulations of four different 2D lattice models: Two standard lattice models and two different constrained models. We also consider a constrained mixed O(3)-RP2 model for values of the parameters such that vector correlations are always disordered. We find that all these models show the same finite-size scaling (FSS) behavior, and therefore belong to the same universality class. However, these FSS curves differ from those computed in the 2D O(3) σ model, suggesting the existence of a distinct 2D RP2 universality class. We also performed simulations for N=4, and the corresponding FSS results also support the existence of an RP3 universality class, different from the O(4) one.