Directed percolation in two dimensions: An exact solution

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dc.creatorChen, L. C.
dc.creatorWu, F. Y.
dc.date2005-11-11
dc.date2005-11-19
dc.date.accessioned2026-07-07T07:37:49Z
dc.date.available2026-07-07T07:37:49Z
dc.descriptionWe 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 $ν=2$.
dc.descriptionFigures now included, one reference added
dc.identifierhttps://arxiv.org/abs/cond-mat/0511296
dc.identifierhttp://arxiv.org/abs/cond-mat/0511296
dc.identifierin "Differential Geometry and Physics", Nankai Tracts in Math. Vol. 10, Eds. M. L. Ge and W. Zhang (World Scientific, Singapore, 2006) pp. 160-168.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/120905
dc.subjectStatistical Mechanics
dc.subjectMathematical Physics
dc.subjectProbability
dc.titleDirected percolation in two dimensions: An exact solution
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