Crossover behavior in the event size distribution of the Olami-Feder-Christensen model

The avalanche size distribution and supercritical toppling value distribution in the Olami-Feder-Christensen model are examined, demonstrating that there exists a crossover value alpha(X) approximately 0.14 for the conservation parameter in the model. We have further confirmed the location of this crossover by identifying upper and lower bounds for alpha(X). For levels of conservation below alpha(X) the asymptotic behavior, in the limit of both infinite-system-size and infinite-precision arithmetic, consists only of avalanches of size 1 with all sites toppling exactly at the threshold value. For larger levels of conservation the probability of finding avalanches of size 2 or bigger remains nonzero in the asymptotic limit.