Directed percolation in two dimensions: An exact solution
Chen, L. C. ; Wu, F. Y.
arXiv, 0511296 / Harvested from arXiv
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 $\nu=2$.
Publié le : 2005-11-11
Classification:  Condensed Matter - Statistical Mechanics,  Mathematical Physics,  Mathematics - Probability
@article{0511296,
     author = {Chen, L. C. and Wu, F. Y.},
     title = {Directed percolation in two dimensions: An exact solution},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0511296}
}
Chen, L. C.; Wu, F. Y. Directed percolation in two dimensions: An exact solution. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0511296/