1202.1153 (Helmut G. Katzgraber et al.)

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

Helmut G. Katzgraber, Katharina Janzen, Creighton K. Thomas

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.

View original: http://arxiv.org/abs/1202.1153