History-dependent percolation in two dimensions

Abstract

We study the history-dependent percolation in two dimensions, which evolves in generations from standard bond-percolation configurations through iteratively removing occupied bonds. Extensive simulations are performed for various generations on periodic square lattices up to side length $L=4096$. From finite-size scaling, we find that the model undergoes a continuous phase transition, which, for any finite number of generations, falls into the universality of standard 2D percolation. At the limit of infinite generation, we determine the correlation-length exponent $1/\nu =0.828(5)$ and the fractal dimension $d_{\mathrm{f}}=1.8644(7)$, which are not equal to $1/\nu =3/4$ and $d_{\mathrm{f}}=91/48$ for 2D percolation. Hence, the transition in the infinite-generation limit falls outside the standard percolation universality and differs from the discontinuous transition of history-dependent percolation on random networks. Further, a crossover phenomenon is observed between the two universalities in infinite and finite generations.

arXiv comment9 pages, 11 figures

References in corpus (18)

• Catastrophic cascade of failures in interdependent networks
• A fast Monte Carlo algorithm for site or bond percolation
• "Explosive Percolation" Transition is Actually Continuous
• Percolation Theory on Interdependent Networks Based on Epidemic Spreading
• Bond and Site Percolation in Three Dimensions
• Recent advances and open challenges in percolation
• Construction and Analysis of Random Networks with Explosive Percolation
• Explosive percolation: a numerical analysis
• Simultaneous analysis of three-dimensional percolation models
• Scaling behavior of explosive percolation on the square lattice
• Convergence of threshold estimates for two-dimensional percolation
• High-precision Monte Carlo study of several models in the three-dimensional U(1) universality class
• Correction-to-scaling exponent for two-dimensional percolation
• Critical fragmentation properties of random drilling: How many random holes need to be drilled to collapse a wooden cube?
• History-dependent percolation on multiplex networks
• Finite-size Scaling of O($n$) Systems at the Upper Critical Dimensionality
• Recursive Percolation
• Bootstrap and diffusion percolation transitions in three-dimensional lattices

Cited by in corpus (4)

• Percolation on complex networks: Theory and application
• Classical-quantum correspondence of special and extraordinary-log criticality: Villain's bridge
• Iterative Site Percolation on Triangular Lattice
• Critical behaviors of cascading dynamics on multiplex two-dimensional lattices