History-dependent percolation in two dimensions

Minghui Hu, Yanan Sun, Dali Wang, Jian-Ping Lv, and Youjin Deng
Phys. Rev. E 102, 052121 – Published 19 November 2020

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 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.

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  • Received 24 May 2020
  • Revised 21 September 2020
  • Accepted 30 October 2020

DOI:https://doi.org/10.1103/PhysRevE.102.052121

©2020 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Minghui Hu1, Yanan Sun1, Dali Wang1, Jian-Ping Lv1,*, and Youjin Deng2,3

  • 1Department of Physics, Anhui Normal University, Wuhu, Anhui 241000, China
  • 2National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
  • 3MinJiang Collaborative Center for Theoretical Physics, Department of Physics and Electronic Information Engineering, Minjiang University, Fuzhou, Fujian 350108, China

  • *jplv2014@ahnu.edu.cn

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Vol. 102, Iss. 5 — November 2020

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