PHASES AND FRACTAL STRUCTURES OF 3-DIMENSIONAL SIMPLICIAL GRAVITY

We study phases and fractal structures of three-dimensional simplicial quantum gravity by a Monte Carlo calculation with a lattice size V = 10(4). After measuring the surface area distribution (SAD) which is th e three-dimensional analog of the loop length distribution (LLD) in tw o-dimensional quantum gravity, we classify the fractal structures into three types: (i) In the strong coupling (hot) phase, strong gravity m akes the space-time one crumpled mother universe with many fluctuating baby universes of small size around it. This is a crumpled phase with a large Hausdorff dimension d(H) = 4.98 +/- 0.05. The topologies of t he sections are extremely complicated. (ii) At the critical point. we observe that the space-time is a pseudo-fractal manifold which has one mother universe with many baby universes of small and middle size aro und it. The Hausdorff dimension d(H) is 3.93 +/- 0.05. We observe some scaling behaviors for the sections of the manifold. This manifold res embles the fractal surface observed in two-dimensional quantum gravity . (iii) In the weak coupling (cold) phase, the mother universe disappe ars completely and the space-time seems to be a branched-polymer with a small Hausdorff dimension d(H) = 1.948 +/- 0.003. almost all of the sections have the spherical topology S-2 in the weak coupling phase. ( C) 1998 Elsevier Science B.V.