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 . 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 and the fractal dimension , which are not equal to and 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.
4 More- Received 24 May 2020
- Revised 21 September 2020
- Accepted 30 October 2020
DOI:https://doi.org/10.1103/PhysRevE.102.052121
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