The weak-coupling limit of simplicial quantum gravity. (English) Zbl 0949.83016
Summary: In the weak-coupling limit, \(\kappa_0 \rightarrow\infty\), 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 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.
MSC:
| 83C27 | Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory |
| 83C45 | Quantization of the gravitational field |
| 52C99 | Discrete geometry |
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