Institut für Theoretische Physik, Universität Leipzig Postfach 100 920, 04009 Leipzig, Germany.
Doctoral College for the Statistical Physics of Complex Systems, Leipzig-Lorraine-Lviv-Coventry (L^{4}), Postfach 100 920, 04009 Leipzig, Germany.
Phys Rev E. 2017 Dec;96(6-1):062125. doi: 10.1103/PhysRevE.96.062125. Epub 2017 Dec 18.
We study long-range power-law correlated disorder on square and cubic lattices. In particular, we present high-precision results for the percolation thresholds and the fractal dimension of the largest clusters as a function of the correlation strength. The correlations are generated using a discrete version of the Fourier filtering method. We consider two different metrics to set the length scales over which the correlations decay, showing that the percolation thresholds are highly sensitive to such system details. By contrast, we verify that the fractal dimension d_{f} is a universal quantity and unaffected by the choice of metric. We also show that for weak correlations, its value coincides with that for the uncorrelated system. In two dimensions we observe a clear increase of the fractal dimension with increasing correlation strength, approaching d_{f}→2. The onset of this change does not seem to be determined by the extended Harris criterion.
我们研究了方形和立方晶格上的长程幂律关联无序。特别是，我们给出了关联强度作为函数的渗流阈值和最大团簇分形维数的高精度结果。关联是使用傅里叶滤波方法的离散版本生成的。我们考虑了两种不同的度量来设置关联衰减的长度标度，表明渗流阈值对这些系统细节非常敏感。相比之下，我们验证了分形维数 d_{f}是一个普遍的量，不受度量选择的影响。我们还表明，对于较弱的关联，其值与无关联系统的相同。在二维中，我们观察到分形维数随关联强度的增加而明显增加，接近 d_{f}→2。这种变化的开始似乎不是由扩展哈里斯准则决定的。
