Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis-CONICET, Chacabuco 917, D5700BWS San Luis, Argentina.
Phys Rev E. 2019 Nov;100(5-1):052104. doi: 10.1103/PhysRevE.100.052104.
The percolation behavior of aligned rigid rods of length k (k-mers) on two-dimensional triangular lattices has been studied by numerical simulations and finite-size scaling analysis. The k-mers, containing k identical units (each one occupying a lattice site), were irreversibly deposited along one of the directions of the lattice. The connectivity analysis was carried out by following the probability R_{L,k}(p) that a lattice composed of L×L sites percolates at a concentration p of sites occupied by particles of size k. The results, obtained for k ranging from 2 to 80, showed that the percolation threshold p_{c}(k) exhibits a increasing function when it is plotted as a function of the k-mer size. The dependence of p_{c}(k) was determined, being p_{c}(k)=A+B/(C+sqrt[k]), where A=p_{c}(k→∞)=0.582(9) is the value of the percolation threshold by infinitely long k-mers, B=-0.47(0.21), and C=5.79(2.18). This behavior is completely different from that observed for square lattices, where the percolation threshold decreases with k. In addition, the effect of the anisotropy on the properties of the percolating phase was investigated. The results revealed that, while for finite systems the anisotropy of the deposited layer favors the percolation along the parallel direction to the alignment axis, in the thermodynamic limit, the value of the percolation threshold is the same in both parallel and transversal directions. Finally, an exhaustive study of critical exponents and universality was carried out, showing that the phase transition occurring in the system belongs to the standard random percolation universality class regardless of the value of k considered.
已通过数值模拟和有限尺寸标度分析研究了长度为 k（k -mer）的取向刚性棒在二维三角晶格上的渗流行为。k-mer 由 k 个相同的单元（每个单元占据一个晶格位置）组成，不可逆地沿晶格的一个方向沉积。通过跟踪由 L×L 个格点组成的格子在占据粒子大小为 k 的粒子的浓度 p 下发生渗流的概率 R_{L,k}(p)，进行连接性分析。对于 k 从 2 到 80 的范围，得到的结果表明，当作为 k-mer 大小的函数绘制时，渗流阈值 p_{c}(k) 呈现出递增函数。p_{c}(k)的依赖性由 p_{c}(k)=A+B/(C+sqrt[k])确定，其中 A=p_{c}(k→∞)=0.582(9) 是无限长 k-mer 的渗流阈值值，B=-0.47(0.21)，C=5.79(2.18)。这种行为与在方格子中观察到的情况完全不同，在方格子中，渗流阈值随 k 减小。此外，还研究了各向异性对渗流相性质的影响。结果表明，虽然对于有限系统，沉积层的各向异性有利于沿平行于取向轴的方向渗流，但在热力学极限下，平行和横向方向的渗流阈值值相同。最后，进行了详尽的临界指数和普遍性研究，结果表明，无论考虑的 k 值如何，系统中发生的相变都属于标准随机渗流普遍性类别。
