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 ↑ ∞.
|Number of pages||11|
|Journal||Physica A: Statistical Mechanics and its Applications|
|Publication status||Published - 2015 Jun 4|
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Condensed Matter Physics