Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
1995-12-09
Phys.Lett. B418 (1998) 273-283
Physics
High Energy Physics
High Energy Physics - Lattice
14 pages, latex file, 5 Postscript figures, use psfig.sty
Scientific paper
10.1016/S0370-2693(97)01320-8
We study phases and fractal structures of three-dimensional simplicial quantum gravity by the Monte-Carlo method. 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 hot (strong coupling) phase, strong gravity makes the space-time one crumpled mother universe with small fluctuating branches around it. This is a crumpled phase with a large Hausdorff dimension $d_{\mbox{\tiny H}} \simeq 5$. The topologies of cross-sections are extremely complicated. (ii) at the critical point, we observe that the space-time is a fractal-like manifold which has one mother universe with small and middle size branches around it. The Hausdorff dimension is $d_{\mbox{\tiny H}} \simeq 4$. We observe some scaling behaviors for the cross-sections of the manifold. This manifold resembles the fractal surface observed in two-dimensional quantum gravity. (iii) in the cold (weak coupling) phase, the mother universe disappears completely and the space-time seems to be the branched-polymer with a small Hausdorff dimension $d_{\mbox{\tiny H}} \simeq 2$. Almost all of the cross-sections have the spherical topology $S^2$ in the cold phase.
Hagura Hiroyuki
Tsuda Noritsugu
Yukawa Tetsuyuki
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