We examine the scaling of geodesic correlation functions in two-dimensional gravity and in spin systems coupled to gravity. The numerical data support the scaling hypothesis and indicate that the quantum geometry develops a non-perturbative length scale. The existence of this length scale allows us to extract a Hausdorff dimension. In the case of pure gravity we find d_H approx. 3.8, in support of recent theoretical calculations that d_H = 4. We also discuss the back-reaction of matter on the geometry.
Catterall, Simon; Thorleifsson, G.; Bowick, Mark; and John, V., "Scaling and the Fractal Geometry of Two-Dimensional Quantum Gravity" (1995). Physics. 491.
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