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

TL;DR

This study explores the conditions for self-organized criticality in spin glasses, revealing it occurs only when the number of neighbors diverges, not in finite-dimensional models.

Contribution

It demonstrates that self-organized criticality in spin systems requires a diverging number of neighbors, challenging previous assumptions of its universality in finite dimensions.

Findings

Self-organized criticality appears only with diverging neighbors.

Finite-dimensional spin glasses do not exhibit SOC.

Large system simulations support the divergence requirement.

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.