Asymptotic Behavior for a Version of Directed Percolation on the Triangular Lattice

Shu Chiuan Chang, Lung Chi Chen

研究成果: Article同行評審

3 引文 斯高帕斯(Scopus)

摘要

We consider a version of directed bond percolation on the triangular lattice such that vertical edges are directed upward with probability y, diagonal edges are directed from lower-left to upper-right or lower-right to upper-left with probability d, and horizontal edges are directed rightward with probabilities x and one in alternate rows. Let t(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), d ∈ [0, 1) but (1 - y)(1 - d) ≠ 1 and aspect ratio α = M/N fixed for the triangular lattice with diagonal edges from lower-left to upper-right, we show that there is an αc = (d-y-dy)/[2(d+y-dy)]+[1-(1-d)2(1-y)2x]/[2(d+ y - dy)2] such that as N → ∞, τ(M, N) is 1, 0 and 1/2 for α > αc, α < αc and α = αc, respectively. A corresponding result is obtained for the triangular lattice with diagonal edges from lower-right to upper-left. We also investigate the rate of convergence of τ(M, N) and the asymptotic behavior of t(M-N, N) and τ(M+N, N) where M-N/N ↑ αc and M+N/N ↓ αc as N ↑ ∞.

原文English
頁(從 - 到)500-522
頁數23
期刊Journal of Statistical Physics
155
發行號3
DOIs
出版狀態Published - 2014 5月

All Science Journal Classification (ASJC) codes

  • 統計與非線性物理學
  • 數學物理學

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