Fractal structure of two-dimensional gravity coupled to c=-2 matter

Abstract

We present the results of numerical calculations of internal fractal dimensions of a dynamically triangulated two-dimensional gravity coupled to c=-2 matter. Internal fractal dimensions as a function of internal geodesic distance are measured from the number of boundaries and the total length of boundaries, and show clear scaling behavior, while the number of triangles starts to scale only around the maximum size. We apply a recursive sampling algorithm for c=-2, which makes it possible to generate the most probable triangulations of spherical topology, consisting of 5\ifmmode\times\else\texttimes\fi{}${10}^{6}$ triangles.