A Neuronal Model at the Edge of Criticality: An Ising-Inspired Approach to Brain Dynamics

Abstract: We present a neuronal network model inspired by the Ising model, where each neuron is a binary spin ($s_i = \pm1$) interacting with its neighbors on a 2D lattice. Updates are asynchronous and follow Metropolis dynamics, with a temperature-like parameter $T$ introducing stochasticity. To incorporate physiological realism, each neuron includes fixed on/off durations, mimicking the refractory period found in real neurons. These counters prevent immediate reactivation, adding biologically grounded timing constraints to the model. As $T$ varies, the network transitions from asynchronous to synchronised activity. Near a critical point $T_c$, we observe hallmarks of criticality: heightened fluctuations, long-range correlations, and increased sensitivity. These features resemble patterns found in cortical recordings, supporting the hypothesis that the brain operates near criticality for optimal information processing. This simplified model demonstrates how basic spin interactions and physiological constraints can yield complex, emergent behavior, offering a useful tool for studying criticality in neural systems through statistical physics.