Abstract
Phases and fractal structures of three-dimensional simplicial quantum gravity are studied 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) a crumpled manifold in the strong coupling (hot) phase with a large Hausdorff dimension d H ⋍ 5 . (ii) a pseudo-fractal manifold at the critical point with a Hausdorff dimension d H ⋍ 4 . We observe some scaling behaviors for the cross-sections of the manifold. (iii) a branched-polymer structure in the weak coupling (cold) phase with a small Hausdorff dimension d H ⋍ 2 .
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