On the robustness of scale invariance in SOC models

A random neighbor extremal stick-slip model is introduced. In the thermodynamic limit, the distribution of states has a simple analytical form and the mean avalanche size, as a function of the coupling parameter, is exactly calculable. The system is critical only at a special point Jc in the coupling parameter space. However, the critical region around this point, where approximate scale invariance holds, is very large, suggesting a mechanism for explaining the ubiquity of scale invariance in Nature.