Tricritical directed percolation in 2+1 dimensions

TL;DR

This paper investigates a generalized 2+1 dimensional directed percolation model, identifying a tricritical point where the nature of the phase transition changes, and compares numerical results with theoretical predictions.

Contribution

It introduces a generalized model with two control parameters and characterizes the tricritical point separating different phase transition behaviors.

Findings

Identification of a tricritical point in the model

Discrepancy between numerical exponents and field theory predictions

Transition from continuous to first-order phase transition

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 L\"ubeck. 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.