发表机构
HUN-REN Centre for Energy Research; HUN-REN Wigner Research Centre for Physics; Universidade de São Paulo（匈牙利研究网络能源研究中心; 匈牙利研究网络维格纳物理研究中心; 圣保罗大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过阈值接触过程模型，发现可激发系统中存在由自发形成的缓慢消失活动簇引起的慢于指数的活动衰减，并指出该现象受晶格维数和小世界特性影响，且衰减稳定性依赖于幂律指数是否超过1/2。
AI 中文摘要
作为可激发自由度相互作用系统的简单模型，我们考虑了各种晶格和网络上的阈值接触过程，其中一次成功的激活事件需要存在多个活跃邻居。我们通过结合数值模拟和现象学理论表明，在两相共存区域且初始活动性足够低的情况下，全局密度的衰减比指数衰减更慢，这是由自发形成的缓慢消失且不通信的活动簇引起的。我们发现这种慢衰减现象通常出现在规则晶格上，也出现在有限维随机晶格（如Voronoi-Delaunay网络）上。然而，小世界特性会阻碍慢衰减，正如在随机正则网络上的模拟所证明的那样。在序参量呈幂律衰减的情况下（该情况在二维规则晶格等中有效），我们的现象学理论指出，只有当衰减指数超过$1/2$时，衰减状态才对无界成核保持稳定。除了众所周知的淬火无序系统的Griffiths效应外，这种源于阈值条件的慢衰减现象提供了另一种非临界但无标度动力学的机制，该机制在不存在无序的情况下也会发生。
英文摘要
As a simple model of interacting systems of excitable degrees of freedom, we consider a threshold contact process on various lattices and networks, in which a successful activation event requires the presence of more than one active neighbors. We show by combining numerical simulations and a phenomenological theory that, in the two-phase coexistence region and for a sufficiently low initial activity, a slower-than-exponential temporal decay of the global density emerges, caused by the spontaneous formation of slowly vanishing and non-communicating clusters of activity. This slow-decay phenomenon is found to appear generally for regular lattices and also for finite-dimensional random lattices such as the Voronoi-Delaunay network. However, the slow-decay is impeded by small-world property, as demonstrated by simulations on random-regular networks. In the case of a power-law decay of the order parameter, which is valid among others on two-dimensional regular lattices, our phenomenological theory points out that the decaying state is stable against unbounded nucleation only if the decay exponent exceeds $1/2$. Besides the well-known Griffiths effects of quenched random systems, this slow-decay phenomenon rooted in the threshold condition provides an alternative mechanism of off-critical but scale-free dynamics, occurring also in the absence of disorder.
Comments15 pages, 16 figures
