  The 2D RP(2) gauge model is studied using the Monte-Carlo Renormalization
Group. We confirm the first-order transition reported by Solomon et al. (PL
112B, (1982)) ending in a critical point associated with vorticity. We find
evidence for a new renormalized trajectory 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 RP(2) but this is illusory and is due to the proximity of the new
renormalized trajectory. We suggest that this is the origin of the
`pseudo'-scaling observed Hasenbusch and Horgan (PR D53, (1996)). We find that
the continuum limit of RP(2) is controlled by the O(3) fixed point. It is
unclear whether the continuum limit of the new renormalized trajectory can be
taken at the observed critical point.
