Max-Planck-Institut für Physik komplexer Systeme, Dresden, Germany.
Phys Rev Lett. 2011 Jun 10;106(23):235702. doi: 10.1103/PhysRevLett.106.235702.
Disorder is an unavoidable ingredient of real systems. Spatial disorder generates Griffiths phases (GPs) which, in analogy to critical points, are characterized by a slow relaxation of the order parameter and divergences of quantities such as the susceptibility. However, these singularities appear in an extended region of the parameter space and not just at a (critical) point, i.e., there is generic scale invariance. Here, we study the effects of temporal disorder, focusing on systems with absorbing states. We show that for dimensions d≥2 there are Temporal Griffiths phases (TGPs) characterized by generic power-law scaling of some magnitudes and generic divergences of the susceptibility. TGPs turn out to be a counterpart of GPs, but with space and time playing reversed roles. TGPs constitute a unifying concept, shedding light on the nontrivial effects of temporal disorder.
无序是真实系统中不可避免的组成部分。空间无序会产生 Griffiths 相（GPs），这些相类似于临界点，其特征是有序参数的缓慢弛豫以及诸如磁化率等量的发散。然而，这些奇点出现在参数空间的扩展区域中，而不仅仅出现在（临界点）处，即存在普适的标度不变性。在这里，我们研究了时间无序的影响，重点研究了具有吸收态的系统。我们表明，对于维度 d≥2，存在时间 Griffiths 相（TGPs），其某些量的标度具有普适的幂律行为，磁化率具有普适的发散。TGPs 的特征是具有普适幂律行为的某些量的标度以及磁化率的普适发散。TGPs 是 GPs 的对应物，但空间和时间扮演着相反的角色。TGPs 构成了一个统一的概念，揭示了时间无序的重要影响。
