title: Boolean decision problems with competing interactions on scale-free networks: critical thermodynamics.
abstract: 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.
authors.affiliation: Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA.
authors.forename: Helmut G
authors.initials: HG
authors.lastname: Katzgraber
authors.forename: Katharina
authors.initials: K
authors.lastname: Janzen
authors.forename: Creighton K
authors.initials: CK
authors.lastname: Thomas