Asymptotic behavior for a version of directed percolation on the honeycomb lattice

Shu Chiuan Chang, Lung Chi Chen

研究成果: Article同行評審

2 引文 斯高帕斯(Scopus)

摘要

We consider a version of directed bond percolation on the honeycomb lattice as a brick lattice such that vertical edges are directed upward with probability y, and horizontal edges are directed rightward with probabilities x and one in alternate rows. Let τ(M,N) be the probability that there is at least one connected-directed path of occupied edges from (0,0) to (M,N). For each x∈(0,1], y∈(0,1] and aspect ratio α=M/N fixed, we show that there is a critical value αc=(1-x+xy)(1+x-xy)/(xy2) such that as N→∞, τ(M,N) is 1, 0 and 1/2 for α>αc, α<αc and α=αc, respectively. We also investigate the rate of convergence of τ(M,N) and the asymptotic behavior of τ(MN-,N) and τ(MN+,N) where MN-/N ↑ αc and MN+/N↓αc as N ↑ ∞.

原文English
頁(從 - 到)547-557
頁數11
期刊Physica A: Statistical Mechanics and its Applications
436
DOIs
出版狀態Published - 2015 6月 4

All Science Journal Classification (ASJC) codes

  • 統計與概率
  • 凝聚態物理學

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