Nature of the continuum limit in the 2D RP² gauge model

The RP² gauge model which allows interpolation between the RP² and O(3) spin models 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 β 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 κ in the range 4-5. The scaling flows are found to give rise to a strong crossover effect between regions of high and low vorticity and are likely to induce an apparent signal for scaling in the crossover region which we propose explains the scaling observed for RP² and RP³ models by Caracciolo et al. and also in a study of the SO(4) matrix model by Hasenbusch and Horgan. We show that the signal for this "pseudo" scaling will occur for the RP² spin model in the crossover region which is precisely the region in which computer simulations are done. We find that the RP² 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. In the former case it is argued that the "vorticity" fixed point controlling the critical behavior terminating the first-order line cannot be identified with the conjectured new renormalized trajectory.