论文标题
自偶会隔离渗透
Self-dual quasiperiodic percolation
论文作者
论文摘要
在没有淬火的随机性的情况下，渗透过渡如何行事？为了解决这个问题，我们研究了两个非随机的自动偶二旋碘模型的方形键渗透模型。在这两个模型中，临界点都具有新出现的离散尺度不变性，但是临界随机渗透的其他额外紧急形式对称性都没有。从关键簇的离散序列中，我们发现两种型号的分形尺寸为$ d_f = 1.911943（1）$和$ d_f = 1.707234（40）$，与$ d_f = 91/48 = 1.89583 ... $ d_f = 91/48 = 1.89583 ... $。通过对圆环上的集群大小和包装概率的数字研究确定的关键指数$ν$也远低于$ν= 4/3 $的随机渗透。尽管这些新模型似乎不属于通用类别，但它们证明了去除随机性如何从根本上改变关键行为。
How does the percolation transition behave in the absence of quenched randomness? To address this question, we study two nonrandom self-dual quasiperiodic models of square-lattice bond percolation. In both models, the critical point has emergent discrete scale invariance, but none of the additional emergent conformal symmetry of critical random percolation. From the discrete sequences of critical clusters, we find fractal dimensions of $D_f=1.911943(1)$ and $D_f=1.707234(40)$ for the two models, significantly different from $D_f=91/48=1.89583...$ of random percolation. The critical exponents $ν$, determined through a numerical study of cluster sizes and wrapping probabilities on a torus, are also well below the $ν=4/3$ of random percolation. While these new models do not appear to belong to a universality class, they demonstrate how the removal of randomness can fundamentally change the critical behavior.
