标题： 接近临界点的神经元模型：受伊辛模型启发的大脑动力学方法 显示英文标题

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

摘要： 我们提出了一种受Ising模型启发的神经网络模型，其中每个神经元是一个二值自旋（$s_i = \pm1$），在二维晶格上与其邻居相互作用。 更新是非同步的，并遵循Metropolis动力学，引入了一个类似温度的参数$T$来增加随机性。 为了融入生理现实，每个神经元都包括固定的开/关持续时间，模仿真实神经元中存在的不应期。 这些计数器防止了立即的再激活，为模型增加了基于生物学的定时约束。 随着$T$的变化，网络从异步活动过渡到同步活动。 在临界点$T_c$附近，我们观察到临界性的标志：波动增强、长程相关性和敏感性增加。 这些特征与皮质记录中发现的模式相似，支持大脑在接近临界状态下运行以实现最佳信息处理的假设。 这个简化的模型展示了基本自旋相互作用和生理约束如何产生复杂的、涌现的行为，为通过统计物理学研究神经系统的临界性提供了一个有用的工具。 显示英文摘要

摘要： 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.