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An Exactly Solvable Anisotropic Directed Percolation Model in Three Dimensions

1998/08/24 by R. Rajesh, Deepak Dhar
Mathematics · Physics and Astronomy · #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physrevlett.81.1646

published as Phys. Rev. Lett., 81 (1998) 1646 · 4 pages, RevTex, 4 figures. 1 reference added, minor changes

openalex publication_date 1998/08/24 · arxiv created 2001/04/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 infinite cluster and hence the direction dependent critical probability. The exponents characterizing the fluctuations of the boundary of the wetted cluster in d dimensions are related to those of the (d\ensuremath-2)-dimensional KPZ equation.

Citations