Cluster geometry and survival probability in systems driven by reaction-diffusion dynamics

We consider a reaction-diffusion model incorporating the reactions A -> 0, A -> 2A and 2A -> 3A. Depending on the relative rates for sexual and asexual reproduction of the quantity A, the model exhibits either a continuous or first-order absorbing phase transition to an extinct state. A tricritical point separates the two phase lines. As well as briefly examining this critical behavior in 2+1 dimensions, we pay particular attention to the cluster geometry. We observe the different cluster structures that form at criticality for the three different types of critical behavior and show that there exists a linear relationship for the probability of survival against initial cluster size at the tricritical point only.