定向有序Janus粒子及其它各向异性系统中渗流的普适临界行为
Universal Critical Behavior of Percolation in Orientationally Ordered Janus Particles and Other Anisotropic Systems
摘要：
我们结合渗流理论和蒙特卡罗模拟，在二维的相互作用的Janus磁盘，自组装成一个取向有序的条纹相在低温下的平衡晶格模型的连接性研究。随着补丁大小的增加或温度的降低，补丁连接的磁盘集群增长，并在阈值处出现一个扩展集群。在条纹相中，临界团簇在平行于条纹的方向上比在垂直方向上延伸得更长，因此渗流是各向异性的。研究发现，在适当的空间尺度下，Janus系统的临界渗流行为与标准各向同性渗流的临界行为是一致的。重标度过程可以应用于理解其他各向异性系统，如对齐的刚性杆和$q$状态Potts模型与各向异性相互作用的渗流。
英文摘要：
We combine percolation theory and Monte Carlo simulation to study in two dimensions the connectivity of an equilibrium lattice model of interacting Janus disks which self-assemble into an orientationally ordered stripe phase at low temperature. As the patch size is increased or the temperature is lowered, clusters of patch-connected disks grow, and a percolating cluster emerges at a threshold. In the stripe phase, the critical clusters extend longer in the direction parallel to the stripes than in the perpendicular direction, and percolation is thus anisotropic. It is found that the critical behavior of percolation in the Janus system is consistent with that of standard isotropic percolation, when an appropriate spatial rescaling is made. The rescaling procedure can be applied to understand other anisotropic systems, such as the percolation of aligned rigid rods and of the $q$-state Potts model with anisotropic interactions.
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