Fig. 11

DFA plot examining the presence of temporal correlations in IAIs. Plot of the average fluctuations $F(n)$ against box size n for IAIs from simulations with $\alpha =w=1$, $h=1/N$ and $N=800$ (a), $N=3200$ (b) and $N=172\text{,}800$ (c). The data is best fit not by a single linear trend but by three lines (red, green, blue) between two crossover points (dashed black lines). For smaller box sizes the Hurst exponents (slope of the line—as annotated next to the individual lines: the DFA exponent α) indicates that correlations extend across these regions. However, for larger box sizes the exponents are closer to 0.5 suggesting that the correlations do not extend across these larger box sizes. With a larger system size (c) the upper crossover point increases to larger box sizes. With increasing system size the system approaches the critical regime—$\lambda =-0.07$ (a), $\lambda =-0.04$ (b) and $\lambda =-0.005$ (c)