Boolean decision problems with competing interactions on scale-free networks: Equilibrium and nonequilibrium behavior in an external bias

Zheng Zhu, Juan Carlos Andresen, M. A. Moore, Helmut G. Katzgraber

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We study the equilibrium and nonequilibrium properties of Boolean decision problems with competing interactions on scale-free networks in an external bias (magnetic field). Previous studies at zero field have shown a remarkable equilibrium stability of Boolean variables (Ising spins) with competing interactions (spin glasses) on scale-free networks. When the exponent that describes the power-law decay of the connectivity of the network is strictly larger than 3, the system undergoes a spin-glass transition. However, when the exponent is equal to or less than 3, the glass phase is stable for all temperatures. First, we perform finite-temperature Monte Carlo simulations in a field to test the robustness of the spin-glass phase and show that the system has a spin-glass phase in a field, i.e., exhibits a de Almeida-Thouless line. Furthermore, we study avalanche distributions when the system is driven by a field at zero temperature to test if the system displays self-organized criticality. Numerical results suggest that avalanches (damage) can spread across the whole system with nonzero probability when the decay exponent of the interaction degree is less than or equal to 2, i.e., that Boolean decision problems on scale-free networks with competing interactions can be fragile when not in thermal equilibrium.

Original languageEnglish
Article number022118
JournalPhysical Review E
Volume89
Issue number2
DOIs
StatePublished - 18 Feb 2014
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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