Memory-induced long-range order in neural activity*

We investigate the relation between memory (time non-locality) and long-range order (LRO) in neuronal dynamics. By means of a cortical dynamics model, we provide both analytical and numerical evidence that memory induces a phase characterized by scale-free distributions of neural activity. The model has two distinct time scales: a fast one related to the coupling (inter-diffusion) of locally coupled neurons and a slow one governing the available resources for neurons. The latter provides a time non-local (memory) effect for the neural activity. LRO emerges when the two time scales are quite distinct. However, when they are comparable, LRO gives way to short-range random behavior. Our findings challenge the current criticality hypothesis in neuroscience.