On the Absence of an Exponential Bound in Four Dimensional Simplicial   Gravity
  We have studied a model which has been proposed as a regularisation for four dimensional quantum gravity. The partition function is constructed by performing a weighted sum over all triangulations of the four sphere. Using numerical simulation we find that the number of such triangulations containing $V$ simplices grows faster than exponentially with $V$. This property ensures that the model has no thermodynamic limit. 
S. Catterall, J. Kogut and R. Renken