Monte-Carlo renormalization group study of gauged RP\u3csup\u3e2\u3c/sup\u3e spin models in two dimensions

The 2D RP2 gauge model is studied using the Monte-Carlo Renormalization Group (MCRG). We confirm the first-order transition reported in [1] ending in a critical point associated with vorticity. We find evidence for a new renormalized trajectory (RT) which is responsible for a cross-over from the vortex dominated regime to the O(3) regime as the coupling is reduced. Near to the cross-over region a good signal for scaling will be observed in RP2 but this is illusory and is due to the proximity of the RT. We suggest that this is the origin of the \u27pseudo\u27-scaling observed in [2]. We find that the continuum limit of RP2 is controlled by the O(3) fixed point