Longone P, Centres P M, Ramirez-Pastor A J
Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis-CONICET, Chacabuco 917, D5700BWS San Luis, Argentina.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jan;85(1 Pt 1):011108. doi: 10.1103/PhysRevE.85.011108. Epub 2012 Jan 4.
The percolation behavior of aligned rigid rods of length k (kmers) on two-dimensional square lattices has been studied by numerical simulations and finite-size scaling analysis. The kmers, containing k identical units (each one occupying a lattice site), were irreversibly deposited along one of the directions of the lattice. The process was monitored 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 1 to 14, show that (i) the percolation threshold exhibits a decreasing function when it is plotted as a function of the kmer size; (ii) for any value of k (k>1), the percolation threshold is higher for aligned rods than for rods isotropically deposited; (iii) the phase transition occurring in the system belongs to the standard random percolation universality class regardless of the value of k considered; and (iv) in the case of aligned kmers, the intersection points of the curves of R(L,k)(p) for different system sizes exhibit nonuniversal critical behavior, varying continuously with changes in the kmer size. This behavior is completely different to that observed for the isotropic case, where the crossing point of the curves of R(L,k)(p) do not modify their numerical value as k is increased.
通过数值模拟和有限尺寸标度分析，研究了长度为k（k聚体）的排列刚性棒在二维正方形晶格上的渗流行为。k聚体包含k个相同单元（每个单元占据一个晶格位点），沿晶格的一个方向不可逆沉积。通过跟踪由L×L个位点组成的晶格在大小为k的粒子占据位点浓度为p时发生渗流的概率R(L,k)(p)来监测该过程。对于k从1到14的结果表明：(i)当渗流阈值作为k聚体大小的函数绘制时，呈现出递减函数；(ii)对于任何k值（k>1），排列棒的渗流阈值高于各向同性沉积棒的渗流阈值；(iii)无论所考虑的k值如何，系统中发生的相变都属于标准随机渗流普适类；(iv)在排列k聚体的情况下，不同系统大小的R(L,k)(p)曲线的交点表现出非普适临界行为，随k聚体大小的变化而连续变化。这种行为与各向同性情况完全不同，在各向同性情况下，R(L,k)(p)曲线的交点不会随着k的增加而改变其数值。
