Universality of the triplet contact process with diffusion

The one-dimensional triplet contact process with diffusion (TCPD) model has been studied using fast multispin GPU Monte Carlo simulations. In particular, the particle density ρ and the density of pairs of neighboring particles ρp have been monitored as a function of time. Mean field predictions for the time evolution of these observables at the critical point are ρ ∼ t−δ and ρp ∼ t−δp with δ = 1/3 and δp = 2/3. We observe that in the vicinity of the critical point of the model, the ratio ρp/ρ tends to a constant, which shows that the one-dimensional TCPD model is not described by mean field behavior. Furthermore, our long simulations allow us to conclude that the mean field prediction of the exponent δ is almost certainly not correct either. Since the crossover to the critical regime is extremely slow for the TCPD model, we are unable to pinpoint a precise value for δ, although we find as an upper bound δ < 0.32. (paper)