We present block analysis, an efficient method of performing finite-size scaling for obtaining the length scale of dynamic heterogeneity and the point-to-set length scale for generic glass-forming liquids. This method involves considering blocks of varying sizes embedded in a system of a fixed (large) size. The length scale associated with dynamic heterogeneity is obtained from a finite-size scaling analysis of the dependence of the four-point dynamic susceptibility on the block size. The block size dependence of the variance of the $\alpha$ relaxation time yields the static point-to-set length scale. The values of the obtained length scales agree quantitatively with those obtained from other conventional methods. This method provides an efficient experimental tool for studying the growth of length scales in systems such as colloidal glasses for which performing finite-size scaling by carrying out experiments for varying system sizes may not be feasible.

中文翻译：

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用于计算玻璃液体中动态和静态长度比例的块分析

我们介绍了块分析，这是一种执行有限尺寸缩放的有效方法，用于获得动态异质性的长度比例和通用玻璃成型液的点到点长度比例。该方法涉及考虑嵌入固定（大）尺寸系统中的各种尺寸的块。通过对四点动态磁化率对块大小的依赖关系进行有限大小的缩放分析，可以获得与动态异质性相关的长度尺度。块大小对方差的依赖$\alpha$松弛时间产生静态的点对点长度标度。所获得的长度标尺的值与从其他常规方法获得的标尺在数量上一致。此方法提供了一种有效的实验工具，用于研究胶体玻璃等系统中长度标度的增长，对于胶体玻璃而言，通过对各种系统尺寸进行实验来执行有限尺寸标度可能是不可行的。