Transitions in nonconserving models of self-organized criticality

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 similar to (alpha(c) - alpha)(-3/2). 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.