Griffiths phase and long-range correlations in a biologically motivated V1 model

Activity in the brain propagates as waves of firing neurons, namely avalanches. These waves' size and duration distributions have been experimentally shown to display a stable power-law profile, long-range correlations and $1/f^{b}$ power spectrum \textit{in vivo} and \textit{in vitro}. We study an avalanching biologically motivated model of mammals visual cortex and find an extended critical-like region -- a Griffiths phase -- characterized by divergent susceptibility and zero order parameter. This phase lies close to the expected experimental value of the \textit{excitatory postsynaptic potential} in the cortex suggesting that critical behavior may be found in the visual system. Avalanches are not perfectly power-law distributed, but it is possible to collapse the distributions and define a cutoff avalanche size that diverges as the network size is increased inside the critical region. The avalanches present long-range correlations and $1/f^{b}$ power spectrum, matching experiments. The phase transition is analytically determined by a mean-field approximation.