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We investigate the conditions required for general spin systems withfrustration and disorder to display self-organized criticality, a propertywhich so far has been established only for the fully-connected infinite-rangeSherrington-Kirkpatrick Ising spin-glass model [Phys. Rev. Lett. 83, 1034(1999)]. Here we study both avalanche and magnetization jump distributionstriggered by an external magnetic field, as well as internal fielddistributions in the short-range Edwards-Anderson Ising spin glass for variousspace dimensions between 2 and 8, as well as the fixed-connectivity mean-fieldViana-Bray model. Our numerical results, obtained on systems of unprecedentedsize, demonstrate that self-organized criticality is recovered only in thestrict limit of a diverging number of neighbors, and is not a generic propertyof spin-glass models in finite space dimensions.

Self-Organized Criticality in Glassy Spin Systems Requires a Diverging Number of Neighbors