The weak-coupling limit of simplicial quantum gravity
In the weak-coupling limit, kappa(0) --> infinity, the partition function of 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 combinatorial triangulation of the D-sphere this limit is 1/D. Defining an ensemble of maximal triangulations, i.e, triangulations that have the maximal possible number of vertices for a given volume, we investigate the properties of this ensemble in three dimensions using both Monte Carlo simulations and a strong-coupling expansion of the partition function, both for pure simplicial 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 fractal properties of this phase. (C) 1999 Elsevier Science B.V. All rights reserved.
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