  We consider a model of p independent Ising spins on a dynamical planar
phi-cubed graph. Truncating the free energy to two terms yields an exactly
solvable model that has a third order phase transition from a pure gravity
region (gamma=-1/2) to a tree-like region (gamma=1/2), with gamma=1/3 on the
critical line. We are able to make an order of magnitude estimate of the value
of p above which there exists a branched polymer (ie tree-like) phase in the
full model, that is, p is approximately 13-23, which corresponds to a central
charge c of about 6-12.
