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 |
| 卷 | 436 |
| DOIs | |
| 出版狀態 | Published - 2015 六月 4 |
指紋
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Condensed Matter Physics
引用此文
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Asymptotic behavior for a version of directed percolation on the honeycomb lattice. / Chang, Shu-Chiuan; Chen, Lung Chi.
於: Physica A: Statistical Mechanics and its Applications, 卷 436, 04.06.2015, p. 547-557.研究成果: Article
TY - JOUR
T1 - Asymptotic behavior for a version of directed percolation on the honeycomb lattice
AU - Chang, Shu-Chiuan
AU - Chen, Lung Chi
PY - 2015/6/4
Y1 - 2015/6/4
N2 - 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 ↑ ∞.
AB - 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 ↑ ∞.
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U2 - 10.1016/j.physa.2015.05.083
DO - 10.1016/j.physa.2015.05.083
M3 - Article
AN - SCOPUS:84930948682
VL - 436
SP - 547
EP - 557
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
SN - 0378-4371
ER -