Integrated information, a measure proposed by Integrated Information Theory as a correlate of conscious experience, behaves as an order parameter that undergoes a phase transition at the critical point in generalized Ising models of small neural networks. In simulations of 159 random, positively weighted five-node excitatory networks, integrated information peaked at the critical temperature, where its generalized susceptibility was maximal. At this point, the system was maximally receptive and responsive to perturbations of its own states. The findings show that integrated information can capture critical behavior in an empirical dataset derived from the generalized Ising model.
Using the critical Ising model of the brain, integrated information—a measure of consciousness—was measured in toy models of generic neural networks. Monte Carlo simulations were run on 159 random weighted networks analogous to small 5-node neural network motifs. Integrated information, as a type of order parameter like magnetism, undergoes a phase transition at the model's critical point, where the system's 'consciousness' is maximally susceptible to perturbations and on the boundary between ordered and disordered forms. This adds evidence that the emergence of consciousness coincides with self-organized criticality, evolution, the emergence of complexity, and the integration of complex systems.