Tricritical directed percolation in 2+1 dimensions

Abstract

We present detailed simulations of a generalization of the Domany-Kinzel model to 2+1 dimensions. It has two control parameters $p$ and $q$ which describe the probabilities $P_k$ of a site to be wetted, if exactly $k$ of its "upstream" neighbours are already wetted. If $P_k$ depends only weakly on $k$, the active/adsorbed phase transition is in the directed percolation (DP) universality class. If, however, $P_k$ increases fast with $k$ so that the formation of inactive holes surrounded by active sites is suppressed, the transition 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 in the contact process studied recently by Lübeck. Critical exponents for it have been calculated previously by means of the field theoretic epsilon-expansion ($\epsilon =3-d$, with $d=2$ in the present case). Rather poor agreement is found with either.

arXiv comment10 pages, including 10 figures; accepted for JSTAT

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