It is proposed that the O(n) spin and geometrical percolation models can help to study the QCD phase diagram due to the universality properties of the phase transition. In this paper, correlations and fluctuations of various sizes of cluster in the Ising model are systematically studied. With a finite size system, we demonstrate how to use the finite size scaling and fixed point behavior to search for critical point. At critical point, the independency of system size is found from skewness and kurtosis of the maximum, second and third largest cluster and their correlations. It is similar to the Binder-ratio, which has provided a remarkable identification of the critical point. Through an explanation of the universal characteristic of skewness and kurtosis of the order parameter, a possible application to the relativistic heavy-ion collisions is also discussed.

中文翻译：

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Ising 渗流跃迁中各种大小簇的临界性质

建议将○(n)由于相变的普遍性，自旋和几何渗流模型有助于研究 QCD 相图。本文系统地研究了 Ising 模型中各种规模的簇的相关性和波动性。对于有限尺寸系统，我们演示了如何使用有限尺寸缩放和定点行为来搜索临界点。在临界点，系统大小的独立性是从最大、第二和第三大集群的偏度和峰度及其相关性中找到的。它类似于 Binder-ratio，它提供了对临界点的显着识别。通过对有序参数的偏度和峰度的普遍特性的解释，还讨论了在相对论重离子碰撞中的可能应用。