Abstract
We present numerical results supporting the existence of an exponential bound in the dynamical triangulation model of three-dimensional quantum gravity. Both the critical coupling and the number of nodes per unit volume show a slow power law approach to the infinite volume limit.
Highlights
Much interest has been generated recently in lattice models for euclidean quantum gravity based on dynamical triangulations [1, 2, 3, 4, 5, 6, 7, 8]
The study of these models was prompted by the success of the same approach in the case of two dimensions, see for example [9]
The primary input to these models is the ansatz that the partition function describing the fluctuations of a continuum geometry can be approximated by performing a weighted sum over all simplicial manifolds or triangulations T
Summary
Much interest has been generated recently in lattice models for euclidean quantum gravity based on dynamical triangulations [1, 2, 3, 4, 5, 6, 7, 8]. The primary input to these models is the ansatz that the partition function describing the fluctuations of a continuum geometry can be approximated by performing a weighted sum over all simplicial manifolds or triangulations T . We can rewrite eqn 1 by introducing the entropy function Ωd (Nd, κ0) which counts the number of triangulations with volume Nd weighted by the node term.
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