Fig. 2: Rydberg excitation incidence curves for different facilitation rates showing power-law growth and Griffiths effects.

a Incidence rate \(C^{\prime}\) versus cumulative incidences C for different facilitation rates κ = {3.3, 4.2, 5.1, 6.0, 6.6, 7.6, 10} kHz (from purple to green). Error bars show the standard error of the mean over typically 16 repetitions of the experiment. The straight dark green line is a power-law fit to a representative dataset yielding the exponent p = 0.59(1). The solid curves are from the simulations of the SIS model on a heterogeneous network and the blue dashed line is a corresponding simulation for a locally homogeneous network for κ = 10 kHz and a comparable system size which gives p ≈ 0.67. b Transition from a subcritical state (\(C^{\prime} \approx 0\)) to an active state (\(C^{\prime} \,> \, 0\)) at late times t = 2 ms as a function of κ. The solid black curve and the dashed blue curve (scaled by a factor of 10 for visual comparison) show simulations of the heterogeneous and locally homogeneous network models, respectively, which exhibit different thresholds and incidence rates. c Characterization of the deceleration of growth parameter p (experimental data points and simulations as a black line) and power-law relaxation exponent α (orange line, numerical simulations only) versus κ. The vertical dashed line indicates the cross-over point between the Griffiths phase (GP) and the active phase. Uncertainties computed from the standard deviation over 100 bootstrap resamplings are shown as error bars except where they are smaller than the data points.