论文标题
集群缩放和关键点：警示性故事
Cluster Scaling and Critical Points: A Cautionary Tale
论文作者
论文摘要
自然界中的许多系统都被认为存在于关键点，包括大脑和地震断层。这种猜想的主要原因是簇（大脑中的雪崩神经元或地震断层中滑动区域的雪崩分布）可以用权力定律描述。因为还有其他机制，例如$ 1/f $噪声可以产生功率定律，因此可以使用群集关键指数满足的其他标准可以用来得出结论，观察到的功率定律行为是否表明了基本的临界点而不是替代机制。我们展示了对群集缩放数据的可能误解如何导致错误地得出结论，即测得的关键指数不满足这些标准。介绍了对一维随机位点渗透和一维ISING模型可能误解数据的示例。我们强调的是，对幂律集群分布的解释表明临界点的存在是微妙的，并且其误解可能导致放弃有前途的研究领域。
Many systems in nature are conjectured to exist at a critical point, including the brain and earthquake faults. The primary reason for this conjecture is that the distribution of clusters (avalanches of firing neurons in the brain or regions of slip in earthquake faults) can be described by a power law. Because there are other mechanisms such as $1/f$ noise that can produce power laws, other criteria that the cluster critical exponents must satisfy can be used to conclude whether or not the observed power law behavior indicates an underlying critical point rather than an alternate mechanism. We show how a possible misinterpretation of the cluster scaling data can lead to incorrectly conclude that the measured critical exponents do not satisfy these criteria. Examples of the possible misinterpretation of the data for one-dimensional random site percolation and the one-dimensional Ising model are presented. We stress that the interpretation of a power law cluster distribution indicating the presence of a critical point is subtle, and its misinterpretation might lead to the abandonment of a promising area of research.
