On the absorbing-state phase transition in the triplet creation model

We study the lattice reaction diffusion model $3A\to 4A$, $A\to\emptyset$ (``triplet creation") using numerical simulations and $n$-site approximations [1]. The simulation results suggest that the phase transition is discontinuous at high diffusion rates. In this regime the order parameter appears to be a discontinuous function of the creation rate; no evidence of a stable interface between active and absorbing phases is found. Based on an effective mapping to a modified compact directed percolation process, we shall nevertheless argue that the transition is {\it continuous} in one dimension, despite the seemingly discontinuous phase transition suggested by studies of finite systems. We also present preliminary results on the phase diagram of the model on the triangular lattice. \\[4pt] [1] G. \'Odor and R. Dickman, J. Stat. Mech. (2009) P08024.