  The RP(2) gauge model is studied in 2D. We use Monte-Carlo renormalization
techniques for blocking the mean spin-spin interaction, <A>, and the mean gauge
field plaquette, <P>. The presence of the O(3) renormalized trajectory is
verified and is consistent with the known three-loop beta-function. The
first-order `vorticity' transition observed by Solomon et al. is confirmed, and
the location of the terminating critical point is established. New scaling
flows in (<A>,<P>) are observed associated with a large exponent kappa in the
range 4~5. The scaling flows give rise to a strong cross-over effect between
regions of high and low vorticity and are likely to induce an apparent signal
for scaling in the cross-over region which we propose explains the scaling
observed for RP(2), RP(3) and SO(4)-matrix models. The signal for this `pseudo'
scaling will occur for the RP(2) spin model in the cross-over region which is
the region in which computer simulations are done. We find that the RP(2) spin
model is in the same universality class as the O(3) spin model but that it is
likely to require a very large correlation length before the true scaling of
this class sets in. We conjecture that the scaling flows are due either to the
influence of a nearby new renormalized trajectory or to the ghost of the
Kosterlitz-Thouless trajectory in the associated XY model.
