Universality of the triplet contact process with diffusion

Abstract: 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 \rho and the density of pairs of neighboring particles \rho_p have been monitored as a function of time. Mean field predictions for the time evolution of these observables in the critical point are \rho\sim t^{-\delta} and \rho_p\sim t^{-\delta_p} with \delta=1/3 and \delta_p=2/3. We observe that in the vicinity of the critical point of the model, the ratio \rho_p/\rho 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 $\delta$ 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 \delta, though we find as an upper bound \delta < 0.32.