Crossover from isotropic to directed percolation

Zongzheng Zhou, Ji Yang, Robert M. Ziff, Youjin Deng

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9 Citations (Scopus)


We generalize the directed percolation (DP) model by relaxing the strict directionality of DP such that propagation can occur in either direction but with anisotropic probabilities. We denote the probabilities as p -=pp d and p -=p(1-p d), with p representing the average occupation probability and p d controlling the anisotropy. The Leath-Alexandrowicz method is used to grow a cluster from an active seed site. We call this model with two main growth directions biased directed percolation (BDP). Standard isotropic percolation (IP) and DP are the two limiting cases of the BDP model, corresponding to p d=1/2 and p d=0,1 respectively. In this work, besides IP and DP, we also consider the 1/2dd=0.6 and 0.8, and determine various critical exponents. These exponents are found to be consistent with those for standard DP. We also determine the renormalization exponent associated with the asymmetric perturbation due to p d-1/2 0 near IP, and confirm that such an asymmetric scaling field is relevant at IP.
Original languageEnglish
Article number021102
Pages (from-to)1-8
Number of pages8
JournalPhysical Review E
Issue number2
Publication statusPublished - 1 Aug 2012
Externally publishedYes

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