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 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 suggests that Boolean decision problems on scale-free
networks are quite stable to local perturbations. Finally, we show that for a
given decay exponent spin glasses on scale-free networks seem to obey
universality. Furthermore, when the decay exponent of the interaction degree is
larger than 4 in the spin-glass sector, the universality class is the same as
for the mean-field Sherrington-Kirkpatrick Ising spin glass.Comment: 14 pages, lots of figures and 2 table
