Directed percolation: mean field theory and series expansions for some two-dimensional lattices
- 1 February 1983
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 16 (2) , 385-404
- https://doi.org/10.1088/0305-4470/16/2/020
Abstract
The shape of percolation clusters in the directed percolation problem is studied within mean field theory. Low-density series expansions are obtained for bond and site problems on the square and triangular lattices. These are used to test a scaling formula for the pair connectedness which involves two lengths xi /sub ///( rho ) and xi perpendicular to ( rho ). Determination of the exponents nu /sub /// and nu perpendicular to for these lengths shows that all four problems are in the same universality class and the values support the hyperscaling relation beta =1/2(D nu perpendicular to + nu /sub ///- gamma ). An independent argument is given for this relation.Keywords
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