The Weak-Coupling Limit of Simplicial Quantum Gravity

Details The Weak-Coupling Limit of Simplicial Quantum Gravity The Weak-Coupling Limit of Simplicial Quantum Gravity

1998-12-23

arxiv.org/abs/hep-lat/9812022v1

Nucl.Phys. B550 (1999) 465-491

Physics

High Energy Physics

High Energy Physics - Lattice

32 pages, latex2e + 17 eps files

Scientific paper

10.1016/S0550-3213(99)00140-6

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.

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