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Center for Nonlinear Studies |
Self-organized criticality (SOC) refers to the tendency of dissipative systems to drive themselves into a scale-invariant critical state without any parameter tuning. These phenomena are of crucial importance because fractal objects displaying SOC are found everywhere, e.g., in earthquakes, the structure of dried-out rivers, the meandering of sea coasts, or in galactic clusters. Understanding its origin, however, represents a major unresolved puzzle. Pioneering work in the 1980s provided insights into the possible origins of SOC: The sandpile and forest-fire models are hallmark examples of dynamical systems that exhibit SOC. However, these models feature ad hoc dynamics, without showing how these can be obtained from an underlying Hamiltonian. The possible existence of SOC was also tested in random magnetic systems, such as Sethna's pioneering work on the random-field Ising model, but in all these, at least one parameter had to be tuned, i.e., no true SOC. The first Hamiltonian model displaying true SOC was the infinite-range mean-field Sherrington-Kirkpatrick spin-glass model. Here, we investigate the conditions required for general disordered magnetic systems to display self-organized criticality. Our results are in disagreement with the traditional lore that self-organized criticality is a property of the mean-field regime of spin glasses. In fact, self-organized criticality is recovered only in the strict limit of a diverging number of neighbors. In light of the aforementioned result, the behavior of damage spreading on scale-free networks, as well as electrons in a disordered landscape (Coulomb glass) are discussed.
Work done in collaboration with Juan Carlos Andresen, Zheng Zhu, Yohanes Pramudya, Creighton K. Thomas, V. Dobrosavljevic, and Gergely T. Zimanyi
Host: Misha Chertkov