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Li, Zhongyang ( , Random Structures & Algorithms)
We study site percolation models on planar lattices including the [
m ,4,n ,4] lattice and the square tilings on the Euclidean plane () or the hyperbolic plane ( ), satisfying certain local constraints on degree‐4 faces. These models are closely related to Ising models and XOR Ising models (product of two i.i.d Ising models) on regular tilings of or . In particular, we obtain a description of the numbers of infinite “+” and “−” clusters of the ferromagnetic Ising model on a vertex‐transitive triangular tiling of for different boundary conditions and coupling constants. Our results show the possibility that such an Ising configuration has infinitely many infinite “+” and “−” clusters, while its random cluster representation has no infinite open clusters. Percolation properties of corresponding XOR Ising models are also discussed. -
Li, Zhongyang ; Liu, Zizhuo ; Aydin, Koray ( , Journal of the Optical Society of America B)
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Yang, Ankun ; Li, Zhongyang ; Knudson, Michael P. ; Hryn, Alexander J. ; Wang, Weijia ; Aydin, Koray ; Odom, Teri W. ( , ACS Nano)