5 papers
Iterated Graph Systems (III): Alexander-Orbach conjecture on hierarchical lattices
Ziyu Neroli
Can the Alexander-Orbach conjecture hold on hierarchical lattices? We construct Gromov-Hausdorff-Prokhorov scaling limits of critical percolation clusters on hierarchical lattices…
Effective-Geometry Rescaling and Universal Critical Behavior in the Anisotropic Three-State Potts Model on the Square Lattice
Fan Yang, Jian Gao, Lu Liu +1
We study the two-dimensional anisotropic three-state Potts ferromagnet on the square lattice using Wolff single-cluster Monte Carlo simulations and finite-size scaling. For couplin…
Moiré Pattern of Rotated Sierpiński Gaskets
Ziyu Neroli
We study the moiré pattern formed by the intersection of a planar Sierpiński gasket and a copy rotated about its centre. At every resonant angle, we prove that the intersection is…
Iterated Graph Systems (I): random walks and diffusion limits
Ziyu Neroli
This paper investigates random walks and diffusion limits on a broad class of fractals generated by Edge Iterated Graph Systems (EIGS), a generalisation of hierarchical lattices. W…
Fractal dimensions for Iterated Graph Systems
Nero Ziyu Li
Building upon [1], this study aims to introduce fractal geometry into graph theory, and to establish a potential theoretical foundation for complex networks. Specifically, we emplo…