2D O(3) + 2D QG

It has been suggested that the peak in the specific heat observed numerically for random surface actions with extrinsic curvature on dynamical lattices might be the result of a low mass bound state in an asymptotically free theory, rather than the signal for a real phase transition. The $O(3)$ model on a fixed lattice displays just such behaviour, but in general transitions appear to be weakened when the models concerned are put on dynamical lattices (ie coupled to 2d quantum gravity). We have therefore performed simulations of the $O(3)$ model on dynamical $\phi^3$ graphs to see if there is still a peak in the specific heat and compared the results with those on fixed lattices.