论文标题
三角形晶格上直的刚性杆的标准和反位点渗透：各向同性和列表沉积/去除
Standard and inverse site percolation of straight rigid rods on triangular lattices: Isotropic and nematic deposition/removal
论文作者
论文摘要
已经进行了数值模拟和有限尺寸的缩放分析，以研究三角形晶格上直杆的标准和逆渗透。在标准（反向）渗透的情况下，晶格最初是空的（占用），线性$ k $ -ser（$ k $线性的连续站点）是随机并顺序沉积在（从晶格中删除），考虑到同型和固定方案。这项研究是通过遵循四个临界浓度的$ k $的行为进行的，该行为$ k $：$ k $：$（i）$ [$（ii）$]标准同型[nematic [nematic]渗透阈值$θ_{c，k} {c，k} $ [$ \ \ vartheta_ {$ \ vartheta_ {c，k} $（III）和$（III），和$（III）和$（IN）各向同性[nematic]渗透阈值$θ^i_ {c，k} $ [$ \ vartheta^i_ {c，k} $]。获得的结果表明：$（1）$ $ $θ_{c，k} $ [$θ^i_ {c，k} $]表现出具有$ k $的非单调依赖性。它减少[增加]，在$ k = 11 $左右的最低限度（最大值），然后增加并渐近地收敛于大的$ k $ $ $ $ $ the的确定价值，c，k \ rightarrow \ rightarrow \ rightarrow \ rightarrow \ infty} = 0.500（2）$ [$θ^i__ { $（2）$ $ \ \ vartheta_ { \ infty} = 0.5334（6）$ [$ \ vartheta^i_ {c，k \ rightarrow \ infty} = 0.4666（6）$]; $（3）$对于这两种型号，相对于$θ= 0.5 $，标准和反渗透阈值的曲线对称。因此，找到了一个补充属性$θ_{c，k} +θ^i_ {c，k} = 1 $（和$ \ \ vartheta_ {c，k} + \ vartheta^i_ {c，k，k} = 1 $），在其他常规及时及时的及时及时及时及时没有观察到。通过使用针对小型系统的配置进行精确枚举，可以在分析上验证此条件。在所有情况下，$（4）$，该模型呈现了整个$ k $的渗透过渡。
Numerical simulations and finite-size scaling analysis have been carried out to study standard and inverse percolation of straight rigid rods on triangular lattices. In the case of standard (inverse) percolation, the lattice is initially empty(occupied) and linear $k$-mers ($k$ linear consecutive sites) are randomly and sequentially deposited on(removed from) the lattice, considering an isotropic and nematic scheme. The study is conducted by following the behavior of four critical concentrations with the size $k$, determined for a wide range of $k$ : $(i)$[$(ii)$] standard isotropic[nematic] percolation threshold $θ_{c,k}$[$\vartheta_{c,k}$], and $(iii)$[$(iv)$] inverse isotropic[nematic] percolation threshold $θ^i_{c,k}$[$\vartheta^i_{c,k}$]. The obtained results indicate that: $(1)$ $θ_{c,k}$[$θ^i_{c,k}$] exhibits a non-monotonous dependence with $k$. It decreases[increases], goes through a minimum[maximum] around $k = 11$, then increases and asymptotically converges towards a definite value for large $k$ $θ_{c,k \rightarrow \infty}=0.500(2)$[$θ^i_{c,k \rightarrow \infty}=0.500(1)$]; $(2)$ $\vartheta_{c,k}$[$\vartheta^i_{c,k}$] rapidly increases[decreases] and asymptotically converges towards a definite value for infinitely long $k$-mers $\vartheta_{c,k \rightarrow \infty}=0.5334(6)$[$\vartheta^i_{c,k \rightarrow \infty}=0.4666(6)$]; $(3)$ for both models, the curves of standard and inverse percolation thresholds are symmetric with respect to $θ= 0.5$. Thus, a complementary property is found $θ_{c,k} + θ^i_{c,k} = 1$ (and $\vartheta_{c,k} + \vartheta^i_{c,k} = 1$), which has not been observed in other regular lattices. This condition is analytically validated by using exact enumeration of configurations for small systems; and $(4)$ in all cases, the model presents percolation transition for the whole range of $k$.
