Tricritical directed percolation in 2+1 dimensions

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 quickly 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 ( = 3 − d, with d = 2 in the present case). Rather poor agreement is found with both.