  We extensively explore networks of weakly unbalanced, leaky
integrate-and-fire (LIF) neurons for different coupling strength, connectivity,
and by varying the degree of refractoriness, as well as the delay in the spike
transmission. We find that the neural network does not only exhibit a
microscopic (single-neuron) stochastic-like evolution, but also a collective
irregular dynamics (CID). Our analysis is based on the computation of a
suitable order parameter, typically used to characterize synchronization
phenomena and on a detailed scaling analysis (i.e. simulations of different
network sizes). As a result, we can conclude that CID is a true thermodynamic
phase, intrinsically different from the standard asynchronous regime.
