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.
Catterall, Simon; Kogut, John B.; and Renken, R., "On the Absence of an Exponential Bound in Four Dimensional Simplicial Gravity" (1994). Physics. 495.
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