Spin glasses on scale-free networks: Simple models to describe opinion formation?

We study the critical behavior of Ising spin glasses on scale-free networks using large-scale Monte Carlo simulations. Our results show that when the exponent that describes the decay of the interaction degree in the scale-free graph is strictly larger than 3 the system undergoes a finite-temperature spin-glass transition. However, when the exponent is equal to or less than 3, the spin-glass phase is stable for all temperatures. This robustness to local (temperature) perturbations and global biases (field) is compared to experimental data from social networks.