Boolean decision problems with competing interactions on scale-free networks: Critical thermodynamics

Details Boolean decision problems with competing interactions on scale-free networks: Critical thermodynamics Boolean decision problems with competing interactions on scale-free networks: Critical thermodynamics

2012-02-06

arxiv.org/abs/1202.1153v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

11 pages, lots of figures and 2 tables

Scientific paper

We study the critical behavior of Boolean variables on scale-free networks with competing interactions (Ising spin glasses). Our analytical results for the disorder/network-decay-exponent phase diagram are verified using large-scale Monte Carlo simulations. When the probability of positive (ferromagnetic) and negative (antiferromagnetic) interactions is the same, the system undergoes a finite-temperature spin-glass transition if the exponent that describes the decay of the interaction degree in the scale-free graph is strictly larger than 3. However, when the exponent is equal to or less than 3, a spin-glass phase is stable for all temperatures. The robustness of both the ferromagnetic and spin-glass phases suggest that Boolean decision problems on scale-free networks are quite stable to local perturbations.

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