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.

翻译：我们提出了一种受伊辛模型启发的神经元网络模型，其中每个神经元是二维晶格上与相邻单元相互作用的二元自旋（$s_i = \pm1$）。更新过程采用异步机制并遵循Metropolis动力学，通过类温度参数$T$引入随机性。为增强生理真实性，每个神经元包含固定的激活/静默持续时间，以模拟真实神经元的不应期。这些计数器阻止即时再激活，为模型添加了基于生物学的时序约束。随着$T$的变化，网络活动从异步状态转变为同步状态。在临界点$T_c$附近，我们观察到临界性的典型特征：增强的涨落、长程关联以及提升的敏感度。这些特征与皮层记录中发现的模式相似，支持了大脑在临界点附近运行以实现最优信息处理的假说。该简化模型展示了基础自旋相互作用与生理约束如何产生复杂的涌现行为，为通过统计物理学研究神经系统的临界性提供了有效工具。