@article{oai:ir.soken.ac.jp:00003346,
 author = {湯川, 哲之 and HAGURA, Hiroyuki and TSUDA, Noritsugu and YUKAWA, Tetsuyuki},
 issue = {3-4},
 journal = {Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics},
 month = {Feb},
 note = {We study phases and fractal structures of three-dimensional simplicial quantum gravity by a Monte Carlo calculation with a lattice size V=104. After measuring the surface area distribution (SAD) which is the three-dimensional analog of the loop length distribution (LLD) in two-dimensional quantum gravity, we classify the fractal structures into three types: (i) In the strong coupling (hot) phase, strong gravity makes 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 dH=4.98±0.05. The topologies of the 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 around it. The Hausdorff dimension dH is 3.93±0.05. We observe some scaling behaviors for the sections of the manifold. This manifold resembles the fractal surface observed in two-dimensional quantum gravity. (iii) In the weak coupling (cold) phase, the mother universe disappears completely and the space-time seems to be a branched-polymer with a small Hausdorff dimension dH=1.948±0.003. almost all of the sections have the spherical topology S2 in the weak coupling phase.},
 pages = {273--283},
 title = {Phases and fractal structures of three-dimensional simplicial gravity},
 volume = {418},
 year = {1998}
}