History-dependent percolation in two dimensions.
basic_science · Level V
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- Record sourced from PubMed, PMID 33327086.
- Also identified by DOI 10.1103/PhysRevE.102.052121.
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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 d_{f}=1.8644(7), which are not equal to 1/ν=3/4 and d_{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.