Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2005-11-11
in "Differential Geometry and Physics", Nankai Tracts in Math. Vol. 10, Eds. M. L. Ge and W. Zhang (World Scientific, Singapor
Physics
Condensed Matter
Statistical Mechanics
Figures now included, one reference added
Scientific paper
We consider a directed percolation process on an ${\cal M}$ x ${\cal N}$ rectangular lattice whose vertical edges are directed upward with an occupation probability y and horizontal edges directed toward the right with occupation probabilities x and 1 in alternate rows. We deduce a closed-form expression for the percolation probability P(x,y), the probability that one or more directed paths connect the lower-left and upper-right corner sites of the lattice. It is shown that P(x,y) is critical in the aspect ratio $a = {\cal M}/{\cal N}$ at a value $a_c =[1-y^2-x(1-y)^2]/2y^2$ where P(x,y) is discontinuous, and the critical exponent of the correlation length for $a < a_c$ is $\nu=2$.
Chen Li-Chyong
Wu Fa Yueh
No associations
LandOfFree
Directed percolation in two dimensions: An exact solution does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Directed percolation in two dimensions: An exact solution, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Directed percolation in two dimensions: An exact solution will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-291847