Tricritical directed percolation in2+1 dimensions

Abstract

We present detailed simulations of a generalization of the Domany–Kinzel model to2+1 dimensions. It has twocontrol parameters, p and q, which describe theprobabilities Pk of a siteto be wetted, if exactly k of its ‘upstream’ neighbours are already wetted. IfPk depends onlyweakly on k, the active/adsorbed phase transition is in the directed percolation (DP) universality class. If, however,Pk increasesquickly with k so that the formation of inactive holes surrounded by active sites is suppressed, thetransition is first order. These two transition lines meet at a tricritical point.This point should be in the same universality class as a tricritical transition inthe contact process studied recently by Lübeck. Critical exponents for it havebeen calculated previously by means of the field-theoretic epsilon-expansion(ϵ = 3 − d,with d = 2 in the present case). Rather poor agreement is found with both.