FRACTAL STRUCTURES OF 3-DIMENSIONAL SIMPLICIAL GRAVITY

Phases and fractal structures of three-dimensional simplicial quantum gravity are studied by the Monte-Carlo method. After measuring the sur face 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 m anifold in the strong coupling (hot) phase with a large Hausdorff dime nsion d(H) similar or equal to 5. (ii) a pseudofractal manifold at the critical point with a Hausdorff dimension d(H) similar or equal to 4. We observe some scaling behaviors for the cross-sections of the manif old. (iii) a branched-polymer structure in the weak coupling (cold) ph ase with a small Hausdorff dimension d(H) similar or equal to 2.