Phase transitions in scale-free neural networks: departure from the standard mean-field universality class.

We investigate the nature of the phase transition from an ordered to a disordered state that occurs in a family of neural network models with noise. These models are closely related to the majority voter model, where a ferromagneticlike interaction between the elements prevails. Each member of the family is distinguished by the network topology, which is determined by the probability distribution of the number of incoming links. We show that for homogeneous random topologies, the phase transition belongs to the standard mean-field universality class, characterized by the order parameter exponent beta=1/2 . However, for scale-free networks we obtain phase transition exponents ranging from 1/2 to infinity. Furthermore, we show the existence of a phase transition even for values of the scale-free exponent in the interval (1.5,2], where the average network connectivity diverges.