集团标度和临界点：一个警示性的故事
Cluster Scaling and Critical Points: A Cautionary Tale
摘要：
自然界中的许多系统都必须存在于临界点，包括大脑和地震断层。这一猜想的主要原因是，群集（大脑中放电神经元的雪崩或地震断层中的滑动区域）的分布可以用幂律来描述。因为存在诸如$1/f$噪声的其他机制可以产生幂律，所以簇临界指数必须满足的其他标准可以用于推断所观察到的幂律行为是否指示潜在的临界点而不是替代机制。我们展示了如何可能的误解的集群缩放数据可能会导致不正确的结论，测得的临界指数不满足这些标准。一维随机点渗流和一维伊辛模型的数据可能被误解的例子。我们强调，幂律簇分布的解释表明存在一个临界点是微妙的，它的误解可能会导致放弃一个有前途的研究领域。
英文摘要：
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.
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