The Weak-Coupling Limit of Simplicial Quantum Gravity

Abstract

In the weak-coupling limit, kappa_0 going to 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.