The weak-coupling limit of simplicial quantum gravity

In the weak-coupling limit, kappa(0) --> infinity, the partition function o f simplicial quantum gravity is dominated by an ensemble of triangulations with the ratio N-0/N-D close to the upper kinematic limit. For a combinator ial triangulation of the D-sphere this limit is 1/D. Defining an ensemble o f maximal triangulations, i.e, triangulations that have the maximal possibl e number of vertices for a given volume, we investigate the properties of t his ensemble in three dimensions using both Monte Carlo simulations and a s trong-coupling expansion of the partition function, both for pure simplicia l gravity and a with a suitable modified measure. For the latter we observe a continuous phase transition to a crinkled phase and we investigate the f ractal properties of this phase. (C) 1999 Elsevier Science B.V. All rights reserved.