Tricritical directed percolation in 2+1 dimensions
Journal of Statistical Mechanics: Theory and Experiment, 2006 (01):
P01004 (Jan 1, 2006)DOI: 10.1088/1742-5468/2006/01/p01004
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 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.