2020/05/31 by Minghui Hu, Yanan Sun, Dali Wang +2
Mathematics · Physics and Astronomy · #Combinatorics #Complex Network Analysis Techniques #Computer science #Condensed matter physics #Continuum percolation theory #Critical exponent #Crossover #Directed percolation #Electrical resistivity and conductivity #Exponent #Geometry #Mathematical physics #Mathematics #Percolation (cognitive psychology) #Percolation critical exponents #Percolation threshold #Physics #Quantum mechanics #Renormalization group #Scaling #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Universality (dynamical systems) #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.102.052121
published as Phys. Rev. E 102, 052121 (2020) · 9 pages, 11 figures
openalex publication_date 2020/11/19 · arxiv created 2020/11/20 · arxiv updated 2020/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 two-dimensional (2D) percolation. At the limit of infinite generation, we determine the correlation-length exponent 1/ν=0.828(5) and the fractal dimension df=1.8644(7), which are not equal to 1/ν=3/4 and df=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.