On the robustness of scale invariance in SOC models

Abstract

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.

6 pages, 4 figures; submitted to Physical Review E; http://link.aps.org/doi/10.1103/PhysRevE.59.4964

References in corpus (7)

• The Limited Scaling Range of Empirical Fractals
• How self-organized criticality works: A unified mean-field picture
• Self-organized criticality as an absorbing-state phase transition
• Gutenberg Richter and Characteristic Earthquake Behavior in Simple Mean-Field Models of Heterogeneous Faults
• Random Neighbor Theory of the Olami-Feder-Christensen Earthquake Model
• Analysis of a dissipative model of self-organized criticality with random neighbors
• On the random neighbor Olami-Feder-Christensen slip-stick model

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