论文标题
历史依赖性渗透在二维
History-dependent percolation in two dimensions
论文作者
论文摘要
我们研究了两个维度的历史依赖性渗透，这几代人从标准的键合构型中通过迭代去除占用的债券而发展。对周期性的正方形晶格至侧长$ L = 4096 $进行了大量的模拟。从有限尺寸的缩放量表中，我们发现该模型经历了连续的相变，对于任何有限的世代数，它都属于标准2D渗透的通用性。在无限生成的限制下，我们确定相关长度指数$ 1/ν= 0.828（5）$和分形维度$ d _ {\ rm f} = 1.864 \，4（7）$，它们不等于$ 1/ν= 3/4 $和$ d_ {因此，无限生成极限的过渡范围不在标准的渗透普遍性之外，并且与随机网络上历史依赖性渗透的不连续过渡不同。此外，在无限和有限世代的两个普遍性之间观察到了跨界现象。
We study the history-dependent percolation in two dimensions, which evolves in generations from standard bond-percolation configurations through iteratively removing occupied bonds. Extensive simulations are performed for various generations on periodic square lattices up to side length $L=4096$. From finite-size scaling, we find that the model undergoes a continuous phase transition, which, for any finite number of generations, falls into the universality of standard 2D percolation. At the limit of infinite generation, we determine the correlation-length exponent $1/ν=0.828(5)$ and the fractal dimension $d_{\rm f}=1.864\,4(7)$, which are not equal to $1/ν=3/4$ and $d_{\rm f}=91/48$ for 2D percolation. Hence, the transition in the infinite-generation limit falls outside the standard percolation universality and differs from the discontinuous transition of history-dependent percolation on random networks. Further, a crossover phenomenon is observed between the two universalities in infinite and finite generations.
