  Four dimensional simplicial gravity has been studied by means of Monte Carlo
simulations for some time, the main outcome of the studies being that the model
undergoes a discontinuous phase transition between an elongated and a crumpled
phase when one changes the curvature (Newton) coupling. In the crumpled phase
there are singular vertices growing extensively with the volume of the system
whereas the elongated phase resembles a branched-polymer.
  We have postulated that this behaviour is a manifestation of the
constrained-mean-field scenario as realised in the Branched Polymer or
Balls-in-Boxes model. These models share all the features of 4D simplicial
gravity except that they exhibit a continuous phase transition. We note here
that this defect can be remedied by a suitable choice of ensemble.
