An Exactly Solvable Anisotropic Directed Percolation Model in Three Dimensions
R. Rajesh, Deepak Dhar
TL;DR
This paper presents an exact solution for a specific anisotropic directed percolation model in three dimensions, revealing the shape of infinite clusters and critical probabilities, and relating boundary fluctuations to KPZ exponents.
Contribution
It introduces an exactly solvable anisotropic directed percolation model in three dimensions and connects boundary fluctuation exponents to KPZ universality.
Findings
Exact solution for the anisotropic directed bond percolation in 3D
Determination of the asymptotic shape of the infinite cluster
Relation of boundary fluctuation exponents to KPZ equation
Abstract
We solve exactly a special case of the anisotropic directed bond percolation problem in three dimensions, in which the occupation probability is 1 along two spatial directions, by mapping it to a five-vertex model. We determine the asymptotic shape of the ininite cluster and hence the direction dependent critical probability. The exponents characterising the fluctuations of the boundary of the wetted cluster in d-dimensions are related to those of the (d-2)-dimensional KPZ equation.
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