论文标题
相互依存网络中混合顺序转变的分形波动
Fractal fluctuations at mixed-order transitions in interdependent networks
论文作者
论文摘要
我们研究了阶参数的波动的几何特征，在随机相互依存的空间网络中混合相变的临界点附近。与连续过渡相反，在临界点处的顺序参数的结构是分形的，在混合顺序跃迁中，该顺序参数的结构已知是紧凑的。值得注意的是，我们发现，尽管紧凑，但接近混合顺序过渡的顺序参数的波动是分形的，直至定义明确的相关长度$ξ'$，在接近临界阈值时会有所不同。我们通过分形维度表征了这些关键波动的自相似性质，$ d_f'= 3D/4 $以及相关长度指数，$ν'= 2/d $，其中$ d $是系统的尺寸。通过渗透和磁化，我们证明了$ d_f' $和$ν'$在任何基础网络的任何$ d $的基础过程的对称性上是独立的。
We study the geometrical features of the order parameter's fluctuations near the critical point of mixed-order phase transitions in randomly interdependent spatial networks. In contrast to continuous transitions, where the structure of the order parameter at criticality is fractal, in mixed-order transitions the structure of the order parameter is known to be compact. Remarkably, we find that although being compact, the fluctuations of the order parameter close to mixed-order transitions are fractal up to a well-defined correlation length $ξ'$, which diverges when approaching the critical threshold. We characterize the self-similar nature of these critical fluctuations through their fractal dimension, $d_f'=3d/4$, and correlation length exponent, $ν'=2/d$, where $d$ is the dimension of the system. By means of percolation and magnetization, we demonstrate that $d_f'$ and $ν'$ are independent on the symmetry of the underlying process for any $d$ of the underlying networks.
