论文标题
在异质网络上具有任意阈值噪声分布的异质网络上伊辛模型的非平衡动力学
Nonequilibrium dynamics of the Ising model on heterogeneous networks with an arbitrary distribution of threshold noise
论文作者
论文摘要
网络上的Ising模型起着基本作用，是理解复杂系统中合作现象的测试基础。在这里，我们在随机图上求解ISING模型的同步动力学，并在高连接限制中具有任意度分布。根据控制微观动力学的阈值噪声的分布，该模型演变为非平衡固定状态。我们获得了一个精确的动力学方程，用于局部磁化的分布，从中我们找到将顺磁性与铁磁相分开的临界线。对于具有负二项式分布的随机图，我们证明了固定的临界行为以及局部磁化的前两个矩的长期临界动力学取决于阈值噪声的分布。特别是，对于代数阈值噪声，这些临界特性取决于阈值分布的幂律尾部。我们进一步表明，每个阶段内平均磁化的松弛时间表现出标准的平均场临界缩放。此处考虑的所有关键指数的值与负二项式分布的方差无关。我们的工作强调了微观动力学对非平衡旋转系统的临界行为的某些细节的重要性。
The Ising model on networks plays a fundamental role as a testing ground for understanding cooperative phenomena in complex systems. Here we solve the synchronous dynamics of the Ising model on random graphs with an arbitrary degree distribution in the high-connectivity limit. Depending on the distribution of the threshold noise that governs the microscopic dynamics, the model evolves to nonequilibrium stationary states. We obtain an exact dynamical equation for the distribution of local magnetizations, from which we find the critical line that separates the paramagnetic from the ferromagnetic phase. For random graphs with a negative binomial degree distribution, we demonstrate that the stationary critical behavior as well as the long-time critical dynamics of the first two moments of the local magnetizations depend on the distribution of the threshold noise. In particular, for an algebraic threshold noise, these critical properties are determined by the power-law tails of the distribution of thresholds. We further show that the relaxation time of the average magnetization inside each phase exhibits the standard mean-field critical scaling. The values of all critical exponents considered here are independent of the variance of the negative binomial degree distribution. Our work highlights the importance of certain details of the microscopic dynamics for the critical behavior of nonequilibrium spin systems.
