  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.
