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

Juan Carlos Andresen, Zheng Zhu, Ruben S. Andrist, Helmut G. Katzgraber, V. Dobrosavljević, and Gergely T. Zimanyi
Phys. Rev. Lett. 111, 097203 – Published 27 August 2013

Abstract

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

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  • Received 14 October 2012

DOI:https://doi.org/10.1103/PhysRevLett.111.097203

© 2013 American Physical Society

Authors & Affiliations

Juan Carlos Andresen1, Zheng Zhu2, Ruben S. Andrist1, Helmut G. Katzgraber2,1, V. Dobrosavljević3, and Gergely T. Zimanyi4

  • 1Theoretische Physik, ETH Zurich, CH-8093 Zurich, Switzerland
  • 2Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA
  • 3Department of Physics and National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32306, USA
  • 4Department of Physics, University of California, Davis, California 95616, USA

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Vol. 111, Iss. 9 — 30 August 2013

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