Matin Sakib, Pun Chon-Kit, Gould Harvey, Klein W
Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
Department of Physics, Clark University, Worcester, Massachusetts 01610, USA.
Phys Rev E. 2020 Feb;101(2-1):022103. doi: 10.1103/PhysRevE.101.022103.
We show that the Olami-Feder-Christensen model exhibits an effective ergodicity breaking transition as the noise is varied. Above the critical noise, the system is effectively ergodic because the time-averaged stress on each site converges to the global spatial average. In contrast, below the critical noise, the stress on individual sites becomes trapped in different limit cycles, and the system is not ergodic. To characterize this transition, we use ideas from the study of dynamical systems and compute recurrence plots and the recurrence rate. The order parameter is identified as the recurrence rate averaged over all sites and exhibits a jump at the critical noise. We also use ideas from percolation theory and analyze the clusters of failed sites to find numerical evidence that the transition, when approached from above, can be characterized by exponents that are consistent with hyperscaling.
我们表明，随着噪声的变化，奥拉米 - 费德 - 克里斯滕森模型呈现出有效的遍历性破缺转变。在临界噪声之上，系统是有效的遍历的，因为每个位点上的时间平均应力收敛到全局空间平均值。相反，在临界噪声之下，各个位点上的应力陷入不同的极限环，系统不是遍历的。为了表征这种转变，我们运用动力系统研究中的思想，并计算递归图和递归率。序参量被确定为所有位点上平均的递归率，并且在临界噪声处出现跳跃。我们还运用渗流理论中的思想，分析失效位点的簇，以找到数值证据表明，当从上方接近转变时，其可以由与超尺度一致的指数来表征。
