We investigate a random-neighbors version of the two dimensional nonconserving earthquake model of Olami, Feder, and Christensen [Phys Rev. Lett. 68, 1244 (1992)]. We show both analytically and numerically that criticality can be expected even in the presence of dissipation. As the critical level of conservation, ${\alpha }_c$, is approached, the cutoff of the avalanche size distribution scales as $\xi \sim ({\alpha }_c-\alpha {)}^{-3\mathrm{}/2}$. The transition from non-SOC to SOC (self-organized criticality) behavior is controlled by the average branching ratio $\sigma$ of an avalanche, which can thus be regarded as an order parameter of the system.

• Received 12 October 1995

DOI:https://doi.org/10.1103/PhysRevLett.76.2326