Figure 1

(a) The spectral dimension as a function of (fictitious) diffusion time $s$ (semilog scale). Crosses represent data points for CDT for simulation with 200 000 simplices, whereas the red solid line represent the fit based of HL gravity. The region where discretium effects are important is lightly shaded. The region where curvature effects dominate is darkly shaded. The intermediate is the ultraviolet continuum region. (b) Zoom into the latter region. (c) Individual residuals for the model fits for 50 000  100 000 and 200 000 simplices. The residuals grow as expected at very small and very large scales under the influence of discretium and curvature effects, respectively. The oscillatory pattern at intermediate scales seems to indicate some systematic deviation from the model, which however, tends to disappear as the number of simplices is increased. For 200 000 simplices the fractional residual remains below 0.5% almost throughout the entire ultraviolet continuum region.Reuse & Permissions