Directed percolation with an absorbing boundary
K. B. Lauritsen, K. Sneppen, M. Markosova, and M. H. Jensen (NBI &, NORDITA, Denmark)
TL;DR
This paper studies directed percolation near an absorbing boundary in 1+1 and 2+1 dimensions, revealing new scaling behaviors and analyzing cluster structures and site distributions affected by the boundary.
Contribution
It introduces new scaling exponents related to standard directed percolation and examines backbone clusters, red bonds, and site distributions along the boundary.
Findings
Distribution of cluster lifetimes and sizes depends on the boundary
New scaling exponents relate to standard directed percolation in 1+1D
Distribution of living sites along the boundary is characterized
Abstract
We consider directed percolation with an absorbing boundary in 1+1 and 2+1 dimensions. The distribution of cluster lifetimes and sizes depend on the boundary. The new scaling exponents can be related to the exponents characterizing standard directed percolation in 1+1 dimension. In addition, we investigate the backbone cluster and red bonds, and calculate the distribution of living sites along the absorbing boundary.
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