We propose a new way of measuring the correlation length in surface growth processes. We define a quantity in d = 1 + 1, where w(t) and L are the surface width of a given sample at time t and the system size, respectively, and ⟨…⟩ denotes the average over samples. The quantity R(L, t) is proportional to the correlation length and follows the relation R(L, t) ∼ t ^1/z before the saturation for various growth models, where z is the dynamic exponent. The applicability of the method was examined for the restricted solid-on-solid (RSOS) model, equilibrium solid-on-solid model, and restricted curvature model. We also estimated z by using the relation R(t) ∼ t ^1/z for the RSOS model in higher dimensions.

我们提出了一种测量表面生长过程中相关长度的新方法。我们在d = 1 + 1 中定义一个数量，其中w ( t ) 和L分别是给定样本在时间t的表面宽度和系统大小，⟨…⟩ 表示样本的平均值。数量R ( L , t ) 与相关长度成正比，并且在各种增长模型的饱和之前遵循关系R ( L , t ) ∼ t ^{1/ z} ，其中z是动态指数。检验了该方法的适用性，包括受限实体对实体 (RSOS) 模型、平衡实体对实体模型和受限曲率模型。我们还预计Ž通过使用关系- [R （吨）〜吨 ^{1 / ž} 在更高维度RSOS模型。